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Luisa MALAGUTI

Professore Ordinario presso: Dipartimento di Scienze e Metodi dell'Ingegneria


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Pubblicazioni

2021 - Saturated Fronts in Crowds Dynamics [Articolo su rivista]
Campos, Juan; Corli, Andrea; Malaguti, Luisa
abstract

We consider a degenerate scalar parabolic equation, in one spatial dimension, of flux-saturated type. The equation also contains a convective term. We study the existence and regularity of traveling-wave solutions; in particular we show that they can be discontinuous. Uniqueness is recovered by requiring an entropy condition, and entropic solutions turn out to be the vanishing-diffusion limits of traveling-wave solutions to the equation with an additional non-degenerate diffusion. Applications to crowds dynamics, which motivated the present research, are also provided


2021 - Wavefronts in Traffic Flows and Crowds Dynamics [Capitolo/Saggio]
Corli, Andrea; Malaguti, Luisa
abstract

In this paper we give an overview of some recent results concerning partial differential equations modeling collective movements, namely, vehicular traffic flows and crowds dynamics. The focus is on traveling-wave solutions to degenerate parabolic equations in one space dimension, even if we briefly discuss models based on different equations. The case of networks is also taken into consideration. The parabolic degeneration opens the possibilities of several different behaviors of the traveling-wave solutions, which are investigated in details.


2020 - NONLOCAL SOLUTIONS AND CONTROLLABILITY OF SCHRODINGER EVOLUTION EQUATION [Articolo su rivista]
Malaguti, L; Yoshii, K
abstract

The paper deals with semilinear evolution equations in complex Hilbert spaces. Nonlocal associated Cauchy problems are studied and the existence and uniqueness of classical solutions is proved. The controllability is investigated too and the topological structure of the controllable set discussed. The results are applied to nonlinear Schrodinger evolution equations with time dependent potential. Several examples of nonlocal conditions are proposed. The evolution system associated to the linear part is not compact and the theory developed in Okazawa-Yoshii [21] for its study is used. The proofs involve the Schauder-Tychonoff fixed point theorem and no strong compactness is assumed on the nonlinear part.


2020 - Uniqueness and nonuniqueness of fronts for degenerate diffusion-convection reaction equations [Articolo su rivista]
Berti, D.; Corli, A.; Malaguti, L.
abstract

We consider a scalar parabolic equation in one spatial dimension. The equation is constituted by a convective term, a reaction term with one or two equilibria, and a positive diffusivity which can however vanish. We prove the existence and several properties of traveling-wave solutions to such an equation. In particular, we provide a sharp estimate for the minimal speed of the profiles and improve previous results about the regularity of wavefronts. Moreover, we show the existence of an infinite number of semi-wavefronts with the same speed.


2019 - Controllability in Dynamics of Diffusion Processes with Nonlocal Conditions [Articolo su rivista]
Malaguti, Luisa; Rykaczewski, Krzysztof; Taddei, Valentina
abstract

The paper deals with semilinear evolution equations in Banach spaces. By means of linear control terms, the controllability problem is investigated and the solutions satisfy suitable nonlocal conditions. The Cauchy multi-point condition and the mean value condition are included in the present discussion. The final configuration is always achieved with a control with minimum norm. The results make use of fixed point techniques; two different approaches are proposed, depending on the use of norm or weak topology in the state space. The discussion is completed with some applications to dynamics of diffusion processes.


2019 - Exact controllability of infinite dimensional systems with controls of minimal norm [Articolo su rivista]
Malaguti, Luisa; Perrotta, Stefania; Taddei, Valentina
abstract

The paper deals with the exact controllability of a semilinear system in a separable Hilbert space. A bounded linear part is considered and a linear control introduced. The state space is compactly embedded in a Banach space and the nonlinear term is continuous in its state variable in the norm of the Banach space. An infinite sequence of finite dimen- sional controllability problems is introduced and the solution is obtained by a limiting procedure. To the best of our knowledge, the method is new in controllability theory. An application to an integro-differential system in euclidean spaces completes the discussion.


2019 - Nonlocal solutions of parabolic equations with strongly elliptic differential operators [Articolo su rivista]
Benedetti, Irene; Malaguti, Luisa; Taddei, Valentina
abstract

The paper deals with second order parabolic equations on bounded domains with Dirichlet conditions in arbitrary Euclidean spaces. Their interest comes from being models for describing reaction–diffusion processes in several frameworks. A linear diffusion term in divergence form is included which generates a strongly elliptic differential operator. A further linear part, of integral type, is present which accounts of nonlocal diffusion behaviours. The main result provides a unifying method for studying the existence and localization of solutions satisfying nonlocal associated boundary conditions. The Cauchy multipoint and the mean value conditions are included in this investigation. The problem is transformed into its abstract setting and the proofs are based on the homotopic invariance of the Leray–Schauder topological degree. A bounding function (i.e. Lyapunov-like function) theory is developed, which is new in this infinite dimensional context. It allows that the associated vector fields have no fixed points on the boundary of their domains and then it makes possible the use of a degree argument.


2019 - Viscous profiles in models of collective movement with negative diffusivity [Articolo su rivista]
Corli, Andrea; Malaguti, Luisa
abstract

In this paper, we consider an advection–diffusion equation, in one space dimension, whose diffusivity can be negative. Such equations arise in particular in the modeling of vehicular traffic flows or crowds dynamics, where a negative diffusivity simulates aggregation phenomena. We focus on traveling-wave solutions that connect two states whose diffusivity has different signs; under some geometric conditions, we prove the existence, uniqueness (in a suitable class of solutions avoiding plateaus) and sharpness of the corresponding profiles. Such results are then extended to the case of end states where the diffusivity is positive, but it becomes negative in some interval between them. Also the vanishing viscosity limit is considered. At last, we provide and discuss several examples of diffusivities that change sign and show that our conditions are satisfied for a large class of them in correspondence of real data.


2017 - An approximation solvability method for nonlocal differential problems in Hilbert spaces [Articolo su rivista]
Benedetti, Irene; Loi, Nguyen V.; Malaguti, Luisa; Obukhovskii, Valeri
abstract

A new approach is developed for the solvability of nonlocal problems in Hilbert spaces associated to nonlinear differential equations. It is based on a joint combination of the degree theory with the approximation solvability method and the bounding functions technique. No compactness or condensivity condition on the nonlinearities is assumed. Some applications of the abstract result to the study of nonlocal problems for integrodifferential equations and systems of integro-differential equations are then showed. A generalization of the result by using nonsmooth bounding functions is given.


2017 - Nonlocal diffusion second order partial differential equations [Articolo su rivista]
Benedetti, Irene; Loi, Nguyen Van; Malaguti, Luisa; Taddei, Valentina
abstract

The paper deals with a second order integro-partial differential equation in RnRn with a nonlocal, degenerate diffusion term. Nonlocal conditions, such as the Cauchy multipoint and the weighted mean value problem, are investigated. The existence of periodic solutions is also studied. The dynamic is transformed into an abstract setting and the results come from an approximation solvability method. It combines a Schauder degree argument with an Hartman-type inequality and it involves a Scorza-Dragoni type result. The compact embedding of a suitable Sobolev space in the corresponding Lebesgue space is the unique amount of compactness which is needed in this discussion. The solutions are located in bounded sets and they are limits of functions with values in finitely dimensional spaces.


2017 - Sharp profiles in models of collective movement. [Articolo su rivista]
Corli, Andrea; DI RUVO, Lorenzo; Malaguti, Luisa
abstract

We consider a parabolic partial differential equation that can be understood as a simple model for crowds flows. Our main assumption is that the diffusivity and the source/sink term vanish at the same point; the nonhomogeneous term is different from zero at any other point and so the equation is not monostable. We investigate the existence, regularity and monotone properties of semi-wavefront solutions as well as their convergence to wavefront solutions.


2017 - Traveling waves for degenerate diffusive equations on networks [Articolo su rivista]
Corli, Andrea; Ruvo, Lorenzo di; MALAGUTI, Luisa; Rosini, Massimiliano D.
abstract

In this paper we consider a scalar parabolic equation on a star graph; the model is quite general but what we have in mind is the description of traffic flows at a crossroad. In particular, we do not necessarily require the continuity of the unknown function at the node of the graph and, moreover, the diffusivity can be degenerate. Our main result concerns a necessary and sufficient algebraic condition for the existence of traveling waves in the graph. We also study in great detail some examples corresponding to quadratic and logarithmic flux functions, for different diffusivities, to which our results apply.


2016 - Nonsmooth feedback controls of nonlocal dispersal models [Articolo su rivista]
Malaguti, Luisa; Rubbioni, Paola
abstract

The paper deals with a nonlocal diffusion equation which is a model for biological invasion and disease spread. A nonsmooth feedback control term is included and the existence of controlled dynamics is proved, satisfying different kinds of nonlocal condition. Jump discontinuities appear in the process. The existence of optimal control strategies is also shown, under suitably regular control functionals. The investigation makes use of techniques of multivalued analysis and is based on the degree theory for condensing operators in Hilbert spaces.


2016 - Semilinear delay evolution equations with measures subjected to nonlocal initial conditions [Articolo su rivista]
Benedetti, I.; Malaguti, Luisa; Taddei, Valentina; Vrabie, I. I.
abstract

We prove a global existence result for bounded solutions to a class of abstract semilinear delay evolution equations with measures subjected to nonlocal initial data of the form: du(t)={Au(t)+f(t,u t )}dt+dg(t) with t∈R+ and u(t)=h(u)(t) for t∈[−τ,0], with τ≥0. The operator A:D(A)⊆X→X is the infinitesimal generator of a C0 -semigroup, f:R+ ×R([−τ,0];X)→X is continuous, g∈BVloc (R+ ;X) and h:Rb (R + ;X)→R([−τ,0];X) is nonexpansive.


2016 - Semi-wavefront solutions in models of collective movements with density-dependent diffusivity [Articolo su rivista]
Corli, Andrea; Malaguti, Luisa
abstract

This paper deals with a nonhomogeneous scalar parabolic equation with possibly degenerate diffusion term; the process has only one stationary state. The equation can be interpreted as modeling collective movements (crowd dynamics, for instance). We show the existence of semi-wavefront solutions for every wave speed; their properties are investigated. Proofs exploit comparison-type techniques and are carried out in the case of one spatial variable; the extension to the general case is straightforward.


2015 - Hartman-type conditions for multivalued Dirichlet problem in abstract spaces [Relazione in Atti di Convegno]
Andres, Jan; Malaguti, Luisa; Pavlačková, Martina
abstract

The classical Hartman’s Theorem in for the solvability of the vector Dirichlet problem will be generalized and extended in several directions. We will consider its multivalued versions for Marchaud and upper-Carath´eodory right-hand sides with only certain amount of compactness in Banach spaces. Advanced topological methods are combined with a bound sets technique. Besides the existence, the localization of solutions can be obtained in this way.


2015 - Nonlocal problems in Hilbert spaces [Relazione in Atti di Convegno]
Benedetti, Irene; Malaguti, Luisa; Taddei, Valentina
abstract

An existence result for differential inclusions in a separable Hilbert space is furnished. A wide family of nonlocal boundary value problems is treated, including periodic, anti-periodic, mean value and multipoint conditions. The study is based on an approximation solvability method. Advanced topological methods are used as well as a Scorza Dragoni-type result for multivalued maps. The conclusions are original also in the single-valued setting. An application to a nonlocal dispersal model is given.


2014 - Nonlocal Problems for Differential Inclusions in Hilbert Spaces [Articolo su rivista]
Irene, Benedetti; Nguyen Van, Loi; Malaguti, Luisa
abstract

An existence theorem for differential inclusions in Hilbert spaces with nonlocal conditions is proved. Periodic, anti-periodic, mean value and multipoint conditions are included in this study. The investigation is based on a combination of the approximation solvability method with Hartman-type inequalities. A feedback control problem associated to a first order partial differential equation completes this discussion.


2014 - Scorza-Dragoni approach to Dirichlet problem in Banach spaces [Articolo su rivista]
Jan, Andres; Malaguti, Luisa; Martina, Pavlacková
abstract

Hartman-type conditions are presented for the solvability of a multivalued Dirichlet problem in a Banach space by means of topological degree arguments, bounding functions, and a Scorza-Dragoni approximation technique. The required transversality conditions are strictly localized on the boundaries of given bound sets. The main existence and localization result is applied to a partial integro-differential equation involving possible discontinuities in state variables. Two illustrative examples are supplied. The comparison with classical single-valued results in this field is also made.


2013 - Dirichlet problem in Banach spaces: the bound sets approach [Articolo su rivista]
Jan, Andres; Malaguti, Luisa; Martina, Pavlackova
abstract

The existence and localization result is obtained for a multivalued Dirichlet problem in a Banach space. The upper-Carathéodory and Marchaud right-hand sides are treated separately because in the latter case, the transversality conditions derived by means of bounding functions can be strictly localized on the boundaries of bound sets.


2013 - Nonlocal semilinear evolution equations without strong compactness: theory and applications [Articolo su rivista]
Irene, Benedetti; Malaguti, Luisa; Taddei, Valentina
abstract

A semilinear multivalued evolution equation is considered in a reflexive Banach space. The nonlinear term has convex, closed, bounded values and a weakly sequentially closed graph when restricted to its second argument. No strong compactness is assumed, neither on the evolution operator generated by the linear part, or on the nonlinear term. A wide family of nonlocal associated boundary value problems is investigated by means of a fixed point technique. Applications are given to an optimal feedback control problem, to a nonlinear hyperbolic integro-differential equation arising in age-structure population models, and to a multipoint boundary value problem associated to a parabolic partial differential equation.


2012 - A Scorza-Dragoni approach to second-order boundary value problems in abstract spaces [Articolo su rivista]
J., Andres; Malaguti, Luisa; M., Pavlačková
abstract

The existence and localization of strong (Carathéodory) solutions is proved for a second-order Floquet problem in a Banachspace. The result is obtained by combining a continuation principle together with a bounding (Liapunov-like) functions approach. Theapplication of the Scorza–Dragoni type technique allows us to use strictly localized transversality conditions.


2012 - Erratum and addendum to "Two-point b.v.p. for multivalued equations with weakly regular r.h.s." [Articolo su rivista]
I., Benedetti; Malaguti, Luisa; Taddei, Valentina
abstract

In this paper, we define a topological index for compact multivalued maps in convex metrizable subsets of a locally convex topological vector space in order to correct the proofs of Theorems 4.1 and 4.2 in Benedetti-Malaguti-Taddei, Nonlinear Anal. 74 (2011) 3657–3670.


2012 - Guiding-like functions for semilinear evolution equations with retarded nonlinearities [Articolo su rivista]
S., Cecchini; Malaguti, Luisa
abstract

The paper deals with a semilinear evolution equation in a reflexive and separable Banach space. The non-linear term is multivalued, upper Caratheodory and it depends on a retarded argument. The existence of global almost exact, i.e. classical, solutions is investigated. The results are based on a continuation principle for condensing multifields and the required transversalities derive from the introduction of suitable generalized guiding functions. As a consequence, the equation has a bounded globally viable set. The results are new also in the lack of retard and in the single valued case. A brief discussion of a non-local diffusion model completes this investigation.


2012 - Semilinear evolution equations in abstract spaces and applications [Articolo su rivista]
I., Benedetti; Malaguti, Luisa; Taddei, Valentina
abstract

The existence of mild solutions is obtained, for a semilinear multivalued equation in a reflexive Banach space. Weakly compact valued nonlinear terms are considered, combined with strongly continuous evolution operators generated by the linear part. A continuation principle or a fixed point theorem are used, according to the various regularity and growth conditions assumed. Applications to the study of parabolic and hyperbolic partial differential equations are given.


2011 - B.v.p. for differential inclusions in Frechét spaces with multiple solutions of the homogeneous problem [Articolo su rivista]
I., Benedetti; Malaguti, Luisa; Taddei, Valentina
abstract

The paper deals with the multivalued boundary value problemx' Є A(t, x)x + F(t, x) for a.a. t Є [a, b], Mx(a)+Nx(b) = 0 in a separable, reflexive Banach space E. The nonlinearity F is weakly upper semicontinuous in x. We prove the existenceof global solutions in the Sobolev space W1,p([a, b], E) with 1 < p < ∞ endowed with the weak topology. We consider the case of multiple solutions of the associated homogeneouslinearized problem. An example completes the discussion.


2011 - Continuous dependence in front propagation for convective reaction-diffusion models with aggregative movements [Articolo su rivista]
Malaguti, Luisa; C., Marcelli; S., Matucci
abstract

The paper deals with a degenerate reaction-diffusion equation, including aggregative movements and convective terms. The model also incorporates a real parameter causing the change from a purely diffusive to a diffusive-aggregativeand to a purely aggregative regime. Existence and qualitative properties of traveling wave solutions are investigated and estimates of their threshold speeds are furnished. Further, the continuous dependence of the threshold wave speed andof the wave profiles on a real parameter is studied, both when the process maintains its diffusion-aggregation nature and when it switches from it to another regime.


2011 - On second-order boundary value problems in Banach spaces: a bound sets approach [Articolo su rivista]
J., Andres; Malaguti, Luisa; M., Pavlačková
abstract

The existence and localization of strong (Carathéodory) solutions is obtained for a second-order Floquet problem in a Banach space. The combination of applied degree arguments and bounding (Liapunov-like) functions allows some solutions to escape from a given set. The problems concern both semilinear differential equations and inclusions. The main theorem for upper-Carathéodory inclusions is separately improved for Marchaudinclusions (i.e. for globally upper semicontinuous right-hand sides) in the form of corollary. Three illustrative examples are supplied.


2011 - On the behavior of periodic solutions of planar autonomous Hamiltonian systems with multivalued periodic perturbations [Articolo su rivista]
O., Makarenkov; Malaguti, Luisa; P., Nistri
abstract

Aim of the paper is to provide a method to analyze the behavior of T-periodic solutions of a perturbed planar Hamiltonian system near a cycle x_0, of smallest period T, of the unperturbed system. The perturbation is represented by a T-periodic multivalued map which vanishes as the parameter tends to zero. In several problems from nonsmooth mechanical systems this multivalued perturbation comes from the Filippovregularization of a nonlinear discontinuous T-periodic term. Through the paper, assuming the existence of a T-periodic solution of the parameterized problems, under the conditionthat x_0 is a nondegenerate cycle of the linearized unperturbed Hamiltonian system, we provide a formula for the distance between any point x_0(t) and the trajectories of the perturbed period solutions along a transversal direction to x_0(t).


2011 - Strictly localized bounding functions and Floquet boundary value problems [Articolo su rivista]
S., Cecchini; MALAGUTI, Luisa; TADDEI, Valentina
abstract

Semilinear multivalued equations are considered, in separable Ba-nach spaces with the Radon-Nikodym property. An effective criterion for the existence of solutions to the associated Floquet boundary value problem is showed. Its proof is obtained combining a continuation principle with a Liapunov-like technique and a Scorza-Dragoni type theorem. A strictly localized transversality condition is assumed. The employed method enables to localize the solution values in a not necessarily invariant set; it allows also to introduce nonlinearities with superlinear growth in the state variable.


2011 - Two-point b.v.p. for multivalued equations with weakly regular r.h.s. [Articolo su rivista]
I., Benedetti; Malaguti, Luisa; Taddei, Valentina
abstract

A two-point boundary value problem associated to a semilinear multivalued evolution equation is investigated, in reflexive and separable Banach spaces. To this aim, an original method is proposed based on the use of weak topologies and on a suitable continuation principle in Fréchet spaces. Lyapunov-like functions are introduced, for proving the required transversality condition. The linear part can also depend on the state variable x and the discussion comprises the cases of a nonlinearity with sublinear growth in x or of a noncompact valued one. Some applications are given, to the study of periodic and Floquet boundary value problems of partial integro-differential equations and inclusionsappearing in dispersal population models. Comparisons are included, with recent related achievements.


2010 - Asymptotic speed of propagation for Fisher-type degenerate reaction-diffusion-convection equations [Articolo su rivista]
Malaguti, Luisa; Ruggerini, Stefano
abstract

The paper deals with the initial-value problem for the degenerate reaction-diffusion-convection equationu_t + h(u)u_x = (u^m)_xx + f(u), x Є R, t>0, m>1,with f, h continuous and f of Fisher-type. By means of comparison type techniques, we prove that the equilibrium u ≡ 1 is an attractor for all solutions with a continuous, bounded, non-negative initial condition u_0(x) = u(x, 0) ≠ 0. Whenu_0 is also compactly supported and satisfies 0 ≤ u0 ≤ 1, the convergence is such that an asymptotic estimate of the interface can be obtained. The employed techniques involve the theory of travelling-wave solutions that we improve in thiscontext. The assumptions on f and h guarantee that the threshold speed wavefront is not stationary and we show that the asymptotic speed of the interface equals this minimal speed.


2010 - Continuous dependence in front propagation of convective reaction-diffusion equations [Articolo su rivista]
Malaguti, Luisa; C., Marcelli; S., Matucci
abstract

Continuous dependence of the threshold wave speed and of thetravelling wave profiles for reaction-diffusion-convection equationsis here studied with respect to the diffusion, reaction and convection terms.


2010 - Semilinear differential inclusions via weak topologies [Articolo su rivista]
I., Benedetti; Malaguti, Luisa; Taddei, Valentina
abstract

The paper deals with the multivalued initial value problem x'(t) Є A(t, x)x+ F (t, x) for a.a. t in[a, b], x(a) = x_0 in a separable, reflexive Banach space E. The nonlinearity F is weakly upper semicontinuous in x and the investigation includes the case when both A and F have asuperlinear growth in x. We prove the existence of local and global classical solutions in the Sobolev space W1,p ([a, b], E) with 1 < p < ∞. Introducing a suitably defined Lyapunov-likefunction, we are able to investigate the topological structure of the solution set. Our main tool is a continuation principle in Frechét spaces and we prove the required pushingcondition in two different ways. Some examples complete the discussion.


2009 - Bound sets approach to boundary value problems for vector second-order differential inclusions [Articolo su rivista]
J., Andres; M., Kozusníková; Malaguti, Luisa
abstract

A continuation principle is established for the solvability of vector second-order boundary value problems associated with upper-Carathéodory differential inclusions. For Floquet second-order problems, this principle is combined with a bound sets approach. The viability result is also obtained in this way.


2009 - On boundary value problems in Banach spaces [Articolo su rivista]
J., Andres; Malaguti, Luisa; Taddei, Valentina
abstract

The paper deals with boundary value problemsassociated to first-order differential inclusions in Banach spaces. The solvability is investigated in the (strong) Carathèodory sense on compact intervals. To this aim, we develop a general method that relies on degree arguments. This method is still combined with a bound sets technique for checking the behavior of trajectories in the neighborhood of a suitable parametric set of candidate solutions. On this basis, we obtain effective criteria for the existence of solutions of Floquet problems. The existence of entirely bounded solutions is also established by means of a sequence of solutions on compact increasing intervals.


2009 - On the Floquet problem for second-order Marchaud differential systems [Articolo su rivista]
J., Andres; M., Kozusníková; Malaguti, Luisa
abstract

Solutions in a given set of the Floquet boundary value problem are investigated for second-order Marchaud systems. The methods used involve a fixed point index techniquedeveloped by ourselves earlier with a bound sets approach. Since the related bounding (Liapunov-like) functions are strictly localized on the boundaries of parameter sets of candidate solutions, some trajectories are allowed to escape from these sets. The main existence and localization theorem is illustrated by two examples for periodic and antiperiodic problems.


2009 - Periodic Solutions of Semilinear Multivalued and Functional Evolution Equations in Banach Spaces [Articolo su rivista]
Cecchini, Simone; Malaguti, Luisa
abstract

This paper deals with the semilinear multivalued evolution equationx'(t) + A(t)x(t) Є F(t, x(t)), t Є [a, b] and x Є E,in an arbitrary Banach space E.The linear operators {A(t) : t Є [a, b]} are densely defined on a common domain in E and generate a strongly continuous evolution system. We discuss the existence of mild periodic solutions, also in the case when the nonlinear term F depends on aretarded argument. We also show that in both cases the solutions set is compact. The proofs are based on topological arguments and make use of the theory of condensing multimaps.


2009 - Strictly localized bounding functions for vector second-order boundary value problems [Articolo su rivista]
J., Andres; Malaguti, Luisa; M., Pavlačková
abstract

The solvability of the second-order Floquet problem in a given set is established by means of C2-bounding functions for vector upper-Carathéodory systems. The applied Scorza-Dragoni type technique allows us to impose related conditions strictly on the boundaries of bound sets. An illustrating example is supplied for a dry friction problem.


2007 - A bounding functions approach to multivalued boundary value problems [Articolo su rivista]
J., Andres; Malaguti, Luisa; Taddei, Valentina
abstract

The solvability of Floquet boundary value problems is investigated for upper-Caratheodory differential inclusions by means of strictly localized C-2-bounding functions. The existence of an entirely bounded solution is obtained in a sequential way. Our criteria can be regarded as a multivalued extension of recent results of Mawhin and Thompson concerning periodic and bounded solutions of Caratheodory differential equations. A simple illustrating example is supplied.


2007 - Aggregative movement and front propagation for bistable population models [Articolo su rivista]
P. K., Maini; Malaguti, Luisa; C., Marcelli; S., Matucci
abstract

Front propagation for aggregation-diffusion-reaction equationsis investigated, with a bistable reaction-term and a diffusion coeffcient with changing sign, modeling aggregating-diffusing processes. We provide necessary and suffcient conditions for the existence of traveling wave solutions and classify them according to how or if they attain their equilibria at finite times. We also show that the dynamics can exhibit the phenomena of finite speed of propagation and/or finite speed of saturation.


2007 - Trends in Differential Equations and Dynamical Systems [Esposizione]
Gavioli, Andrea; Malaguti, Luisa; Villarini, Massimo
abstract

The workshop took place at Modena, from November 29th to 30th.The main speakers were J. Andres, from Palachy University (Olomouc, SK), P. K. Maini, from the University of Oxford (UK), V. Obukhovskii, from Voronezh State University (Russia), and other speakers from Italy (R. Johnson, F. Papalini, M. Tarallo). Furthermore, several talks were given by young researchers. The topics of the meeting covered many different areas in the field of differential equations and related problems. In particular, here are some of the exposed subjects: front-propagation in reaction-diffusion equations, which often arise from biological models, Sturm-Liouville operators, perturbation theory for Hamiltonian systems, impulsive control systems, boundary value problems and the theory of bound sets, delay equations, differential inclusions.


2006 - Diffusion-aggregation processes with mono-stable reaction terms [Articolo su rivista]
P. K., Maini; Malaguti, Luisa; C., Marcelli; S., Matucci
abstract

This paper analyses front propagation of the aggregation-diffusion-reaction equation with a monostable reaction term and a diffusion coefficient which changes sign from positive to negative values. This model equation accounts for simultaneous diffusive and aggregative behaviors of a population dynamic depending on the population density. The existence of infinitely many traveling wave solutions is proven. These fronts are parameterized by their wave speed and monotonically connect the stationary states 0 and 1. In the degenerate case sharp profiles appear, corresponding to the minimum wave speed. They also have new behaviors, in addition to those already observed in diffusive models, since they can be right compactly supported, left compactly supported, or both. The dynamics can exhibit, respectively, the phenomena of finite speed of propagation, finite speed of saturation, or both.


2005 - Finite speed of propagation in monostable degenerate reaction-diffusion-convection equations [Articolo su rivista]
Malaguti, Luisa; C., Marcelli
abstract

We study the existence and properties of travelling wave solutions of the Fisher-KPP reaction-diffusion-convection equation u_t + h(u)u_x = [D(u)u_x]_x + g(u), where the diffusivity D(u) is simply or doubly degenerate. Both the cases when D(0) and D(1) are possibly zero real values or infinity, are treated. We discuss the effects, due to the presence of a convective term, concerning the property of finite speed of propagation. Moreover, in the doubly degenerate case we show the appearance of new types of profiles and provide their classification according to sharp relations between the nonlinear terms of the model. An application is also presented, concerning the evolution of a bacterial colony.


2005 - Fixed point analysis for non-oscillatory solutions of quasi linear ordinary differential equations [Articolo su rivista]
Malaguti, Luisa; Taddei, Valentina
abstract

The paper deals with a quasi-linear ordinarydifferential equation when the nonlinearity is not necessarily monotone in its second argument. We find necessary and sufficient conditions for the existence of unbounded non-oscillatory solutions. By means of a fixed point technique we investigate their growth, proving the coexistence of solutions with different asymptotic behaviors. In some special cases we are able to show the exact asymptotic growth of these solutions. We apply previous analysis for studying the non-oscillatory problem. Several examples are included.


2005 - On transitional solutions of second order nonlinear differential equations [Articolo su rivista]
Malaguti, Luisa; C., Marcelli; N., Partsvania
abstract

The paper deals with the existence of bounded solutions of the nonlinear diferential equation u''=f(t,u,u') satisfying suitable conditions at infinity. New existence results are obtained, which generalize and unify previous quoted investigations. The main technique for proving all the results derives from the comparison-type theory introduced by Kiguradze and Shekhter.


2005 - The effects of convective processes on front propagation in various reaction-diffusion equations [Relazione in Atti di Convegno]
Malaguti, Luisa; Marcelli, C.; Matucci, S.
abstract

We present a brief survay on our recent results concerning the existence and properties of travelling wave solutions to reaction-diffusion-convection equations with different types of reaction terms. In particular, we show that in certain cases the presence of an additional transport term causes the disappearance of wavefronts.


2005 - Trends in Differential Equations and Dynamical Systems [Esposizione]
Gavioli, Andrea; Malaguti, Luisa; Villarini, Massimo
abstract

The workshop took place at Reggio Emilia, from September 29th to 30th. The main speakers were S. Kamin from Tel-Aviv University, Tel-Aviv (Israel) and L. Sanchez from Lisbon University (Lisbon, Portugal) and other speakers from Italy (A. Agrachev and S. Terracini). Furthermore, several talks were given by young researchers. The topics of the meeting covered many different areas in the field of differential equations and control problems.


2004 - Bounded solutions and wavefronts for discrete dynamics [Articolo su rivista]
Malaguti, Luisa; P., Rehak; Taddei, Valentina
abstract

This paper deals with the second-order nonlinear difference equation Delta(r(k)Deltau(k)) + q(k)g(u(k+1)) = 0 where {r(k)} and {q(k)} are positive real sequences defined on N, and the nonlinearity g : R --> R is nonnegative and nontrivial. Sufficient and necessary conditions are given, for the existence of bounded solutions starting from a fixed initial condition u(0). The same dynamic, with f instead of g such that uf (u) > 0 for u not equal 0, was recently extensively investigated. On the contrary, our nonlinearity g is of a small appearance in the discrete case. Its introduction is motivated by the analysis of wavefront profiles in biological and chemical models. The paper emphasizes the many different dynamical behaviors caused by such a g with respect to the equation involving function f. Some applications in the study of wavefronts complete this work.


2004 - Front propagation in bistable reaction-diffusion-advection equations [Articolo su rivista]
Malaguti, Luisa; C., Marcelli; S., Matucci
abstract

The paper deals with the existence and properties of frontpropagation between the stationary states 0 and 1 of the reaction-diffusion-advection equation with a bistable reaction term G and a strictly positive diffusive process. We show that the additional transport term h can cause the disappearance of such wavefronts and prove that their existence depends both on the local behavior of G and h near the unstable equilibrium and on a suitable sign condition on h in [0, 1]. We also provide an estimate of the wave speed, which can be negative unlike what happens to the mere reaction-diffusion dynamic occurring when h ≡ 0.


2003 - A unifying approach to travelling wavefronts for reaction-diffusion equations arising from genetics and combustion models [Articolo su rivista]
Malaguti, Luisa; C., Marcelli; S., Matucci
abstract

We present a new approach for investigating the existence of travelling wave solutions of the reaction-diffusion equation with density dependent diffusion. Such an apporach allows to treat contemporarily different types of reaction terms which frequently appear in genetics and combustion models.


2003 - Bounded solutions of Carathéodory differential inclusions: a bound sets approach [Articolo su rivista]
J., Andres; Malaguti, Luisa; Taddei, Valentina
abstract

A bound sets technique is developed for Floquet problems to Carathèodory differential inclusions. It relies on the construction of either continuous or locally Lipschitzian Lyapunov-like bounding functions. Proceeding sequentially, the existence of bounded trajectories is then obtained. Nontrivial examples are supplied to illustrate our approach.


2003 - Existence and multiplicity of heteroclinic solutions for non-autonomous boundary eigenvalue problem [Articolo su rivista]
Malaguti, Luisa; C., Marcelli
abstract

In this paper we investigate the boundary eigenvalue problem x''-b(c,t,x)x'+g(t,x)=0, x(-∞)=0, x(+∞)=1 depending on the real parameter c. We take the function b continuous and positive and assume that g is bounded and becomes active and positive only when it exceeds a threshold value theta in (0,1). At the point theta we allow g to have a jump. Additional monotonicity properties are required, when needed. Our main discussion deals with the non-autonomous case. In this context we prove the existence of a continuum of values for which this problem is solvable and we estimate the interval of such admissible values. In the autonomous case, we show its solvability for at most one c*. In the special case when b=c+h(x) with h continuous, we also give a non-existence result, for any real c. Our methods combine comparison-type arguments, both for first and second order dynamics, with a shooting technique. Some applications of the obtained results are included.


2003 - On a two-point boundary value problem for the second order ordinary differential equations with singularities [Articolo su rivista]
A., Lomtatidze; Malaguti, Luisa
abstract

The paper deals with the boundary value problemu''= f(t; u; u'), u(a+) = 0; u(b−) = 0, where f is a real-valued function defined on (a; b) × R× R and it is Caratheodory on (a +c ; b −c) × R× R for any small c>0.


2003 - Sharp profiles in degenerate and doubly-degenerate Fisher-KPP equations [Articolo su rivista]
Malaguti, Luisa; C., Marcelli
abstract

This paper investigates the effects of a degenerate diffusion term in reaction-diffusion models ut=[D(u)ux]x + g(u) with Fisher-KPP type g. Both in the case when D(0) = 0 and when D(0) = D(l) = 0, with D(u) > 0 elsewhere, we obtain a continuum of travelling wave solutions having wave speed c greater than a threshold value c* and we show the appearance of a sharp-type profile when c = c*. These results solve recent conjectures formulated by Sanchez-Garduno and Maini (J. Differential Equations 117 (1995) 281) and Satnoianu et al. (Discrete Continuous Dyn. Systems (Series B) 1 (2000) 339).


2003 - The influence of convective effects on front propagation in certain diffusive models [Relazione in Atti di Convegno]
Malaguti, Luisa; Marcelli, C.
abstract

We consider a reaction-diffusion-convection equation where the reaction term well describes those phenomena which activate only after a certain threshold value. We address our interest in the existence of travelling wave solutions (t.w.s.) between two equilibria and their corresponding wave sppeds. We show that, when the convective term H is, in some sense, weak, this model behaves as in the absence of convection and it admits a unique (up to space shifts) t.w.s. with a positive wave speed. On the contrary, when H prevails over the other terms, no t.w.s. exists.


2003 - Wave fronts in reaction-diffusion equations [Relazione in Atti di Convegno]
Malaguti, Luisa; C., Marcelli; S., Matucci
abstract

A new approach, based on upper and lower solutions, was recently employed by the same authors to unify and generalize existing results for wave fronts in reaction-diffusion equations arising in combustion and genetic models. The statement of the problem and then main results are here explaned, and relations with existing results are analyzed. Some open problems and directions for futurre research are also indicated.


2002 - Heteroclinic Orbits in Plane Dynamical Systems [Articolo su rivista]
Malaguti, Luisa; C., Marcelli
abstract

We consider general second order boundary value problems on the whole line of the type u''=h(t, u, u'), u(-∞)=0, u(+∞)=1, for which we provide existence, non-existence, multiplicity results. The solutions we find can be reviewed as heteroclinic orbits in the (u, u') plane dynamical system.


2002 - Travelling wavefronts in reaction-diffusion equations with convection effects and non-regular terms [Articolo su rivista]
Malaguti, Luisa; C., Marcelli
abstract

This paper deals with the appearance of monotone bounded travelling wave solutions for a parabolic reaction-diffusion equation which frequently meets both in chemical and biological systems. In particular, we prove the existence of monotone front type solutions for any wave speed c greater than or equal to c* and give an estimate for the threshold value c*. Our model takes into account both of a density dependent diffusion term and of a non-linear convection effect. Moreover, we do not require the main non-linearity g to be a regular C1 function; in particular we are able to treat both the case when g'(0) = 0, giving rise to a degenerate equilibrium point in the phase plane, and the singular case when g'(0) = +∞. Our results generalize previous ones due to ARONSON and WEINBERGER [Adv. Math. 30 (1978), pp. 33 - 76], GIBBS and MURRAY (see MURRAY [Mathematical Biology, Springer-Verlag, Berlin, 1993]) and MCCABE, LEACH and NEEDHAM [SIAM J. Appl. Math. 59 (1998), pp. 870-899]. Finally, we obtain our conclusions by means of a comparison-type technique which was introduced and developed in this framework in a recent paper by the same authors.


2001 - Floquet Boundary Value Problems for Differential Inclusions: a Bound Sets Approach [Articolo su rivista]
J., Andres; Malaguti, Luisa; Taddei, Valentina
abstract

A technique is developed for the solvability of the Floquet boundary value problem associated to a differential inclusion. It is based on the usage of a not necessarily C-1-class of Liapunov-like bounding functions. Certain viability arguments are applied for this aim. Some illustrating examples are supplied.


2001 - The rational expectation dynamics of a model for the term structure and monetary policy [Articolo su rivista]
Malaguti, Luisa; Torricelli, Costanza
abstract

In the present paper we set up a rational expectation model for the interaction between the expectation theory of the term structure, monetary policy and a time-varying premium. The results we obtain allow to conclude that the information content of the spread over the short/long rate depends onwhether or not the joint working of monetary policy and the time-varyingterm premium, which is peculiar to our model, exactly compensate the classicalimplication of the Expectation Theory. So our results can rationalise regression testsobtaining small or even negative values for the spread coefficient.


2000 - Existence of Bounded Trajectories Via Upper and Lower Solutions [Articolo su rivista]
Malaguti, Luisa; C., Marcelli
abstract

The paper deals with the boundary value problem (on the whole line) u''-f(u,u')+g(u)=0, u(-∞)=0, u(+∞)=1, where g is a continuous non-negative function with support [0, 1], and f is a continuous function. By means of a new approach, based on a combination of lower and upper-solutions methods and phase-plane techniques, we prove an existence result for the problem when f is superlinear in u'; by a similar technique, we also get a non-existence one. As an application, we investigate the attractivity of the singular point (0,0) in the phase-plane (u, u'). Applications of these results in the field of front-type solutions for reaction diffusion equations can be found in L. Malaguti, C. Marcelli, Math. Nachr. 242 (2002), 148—164


2000 - On a Nonlocal Boundary Value Problem for Second Order Nonlinear Singular Differential Equations [Articolo su rivista]
A., Lomtatidze; Malaguti, Luisa
abstract

Criteria for the existence and uniqueness of a solution of a nonlocal second order boundary value problem are estabilished. These criteria apply, in particular, to the case when the nonlinearity has nonintegrable singularities.


2000 - Viable solutions of differential inclusions with memory in Banach spaces [Articolo su rivista]
Gavioli, Andrea; Malaguti, Luisa
abstract

In this paper we study functional differential inclusions with memory and state constraints. We assume the state space to be a separable Banach space and prove existence results for an upper semicontinuous orientor field; we consider both the case of a globally measurable orientor field and the case of a Caratheodory one.


1999 - A comparison-type approach for travelling fronts [Relazione in Atti di Convegno]
Malaguti, Luisa; C., Marcelli
abstract

We propose a new approach, based on differential inequalities, in order to study travelling wave solutions for a diffusion equation u_t=u_xx+g(u) with g having compact support and positive inside it. We are able to consider any arbitrary continuous non-linear term g; in particular we do not need to assume a linear growth condition on g, even of local type.


1998 - Asymptotic properties of an ordinary differential equation via topological methods [Articolo su rivista]
Malaguti, Luisa; Taddei, Valentina
abstract

The existence of bounded and unbounded solutions for a second order equation is obtained via topological methods


1997 - Monetary policy and the term structure of interest rates: a generalization of McCallum model [Capitolo/Saggio]
Malaguti, Luisa; Torricelli, Costanza
abstract

McCallum (1994) sets up a Rational Expectation model for the interaction of monetary policy and the Expectation Theory of the term structure which rationalises some empirical failures of the latter and demonstrates the inappropriateness of usual regression tests for the information in the term structure. In the present paper, we generalize McCallum (1994) two-period model by introducing a different, finance-theoretic characterization of the term premium. Our results still account for those empirical findings which are at odds with the Expectation Theory of the term structure and yet support validity of usual regressions performed to assess the information content of the term structure. Our results depend on the relative magnitude of the relevant parameters in the model and therefore final conclusions have to be left to empirical investigations.


1996 - Monotone Trajectories of Differential Inclusions in Banach Spaces [Articolo su rivista]
Malaguti, Luisa
abstract

Existence results are obtained for monotone trajectories of nonlinear differential inclusions in a separable Banach space. They extend in two directions previous ones due to Aubin-Cellina, Deimling and Haddad.


1996 - Optimal Solutions in a Growth Model with Irreversible Investments [Articolo su rivista]
Malaguti, Luisa
abstract

We consider an economical model where a single commodity can be either consumed or invested. We assume that investments are irreversible and study the problem of maximizing a disconted utility functional on an unbounded time interval. Using existence theorems for infinite-horizon optimal control problmes, we prove the existence of strongly optimal solutions. The result obtained generalizes a previous one due to Arrow-Kurz.


1995 - Bounded Solutions For a Class of Second Order Nonlinear Differential Equations, Differential Equations and Dynamical Systems [Articolo su rivista]
Malaguti, Luisa
abstract

An existence result of bounded solutions with assigned initial conditions for a second order differential equation is given. The techniques applied are then used to solve a boundary value problem suggested both by the theory of population genetics and by the study of combustion models.


1995 - Limit Properties for Solutions of a Class of Second Order Nonlinear Differential Equations [Articolo su rivista]
Malaguti, Luisa
abstract

The paper deals wtih the boundedness and the asymptotic behaviour of the solutions of a second order differential equation which is nonlinear in the solution variable. The considered equation was suggested both by the theory of population genetics and by the study of combustion models.


1987 - Soluzioni periodiche dell’equazione di Liénard: biforcazione dall’infinito e non unicità [Articolo su rivista]
Malaguti, Luisa
abstract

The paper deals with non-existence and non-uniqueness results for periodic solutions of the Liénard equation.


1987 - Sull'ampiezza della soluzione periodica in un modello non lineare del ciclo economico [Relazione in Atti di Convegno]
Malaguti, Luisa
abstract

Si studia un modello non lineare di ciclo economico del tipo moltiplicatore-accelleratore nel quale le oscillazioni si ottengono dalle interazioni tra il reddito e l'investimento. Da un punto di vista matematico si tratta di una equazione differenziale non lineare del secondo ordine del tipo Lienard. L'uso della teoria classica su questa classe di equazioni consente di mostrare la presenza di una unica soluzione periodica, che risulta un ciclo limite stabile. Il modello contiene un parametro reale, che dipende dal fenomeno economico cosiddetto dell'accelleratore e l'indagine prosegue con uno studio dettagliato dell'ampiezza del ciclo al variare di questo parametro.


1985 - Su alcune congetture nel modello di Goodwin [Relazione in Atti di Convegno]
Malaguti, Luisa
abstract

Il modello del sistema capitalistico elaborato da R.M. Goodwin nel 1967 si propone di cogliere le fluttuazioni dinamiche delle principali variabili macroeconomiche. Il ciclo viene, qui, visto come un effetto naturale delle contraddizioni interne al capitalismo. Per gli agenti economici, lavoratori e capitalisti, queste continue oscillazioni non sono vantaggiose ed e', quindi, ragionevole attendersi che essi si sforzino di contrastarle. Il punto stazionario verso il quale cercano di portare l'economia e', pero', diverso per le due classi sociali. Scopo del lavoro e' analizzare il comportamento asintotico del processo economico soggetto a questo fenomeno di conflittualita' mediante l'uso degli strumenti che sono propri della Teoria dei Giochi.