
DIEGO BERTI
Docente a contratto Dipartimento di Scienze e Metodi dell'Ingegneria

Home 
Curriculum(pdf) 
Didattica 
Pubblicazioni
2022
 Diffusion–convection reaction equations with signchanging diffusivity and bistable reaction term
[Articolo su rivista]
Berti, Diego; Corli, Andrea; Malaguti, Luisa
abstract
We consider a reaction–diffusion equation with a convection term in one space variable, where the diffusion changes sign from the positive to the negative and the reaction term is bistable. We study the existence of wavefront solutions, their uniqueness and regularity. The presence of convection reveals several new features of wavefronts: according to the mutual positions of the diffusivity and reaction, profiles can occur either for a single value of the speed or for a bounded interval of such values; uniqueness (up to shifts) is lost; moreover, plateaus of arbitrary length can appear; profiles can be singular where the diffusion vanishes.
2021
 Wavefronts for degenerate diffusionconvection reaction equations with signchanging diffusivity
[Articolo su rivista]
Berti, Diego; Corli, Andrea; Malaguti, Luisa
abstract
We consider in this paper a diffusionconvection reaction equation in one space dimension. The main assumptions are about the reaction term, which is monostable, and the diffusivity, which changes sign once or even more than once; then, we deal with a forwardbackward parabolic equation. Our main results concern the existence of globally defined traveling waves, which connect two equilibria and cross both regions where the diffusivity is positive and regions where it is negative. We also investigate the monotony of the profiles and show the appearance of sharp behaviors at the points where the diffusivity degenerates. In particular, if such points are interior points, then the sharp behaviors are new and unusual.
2020
 Uniqueness and nonuniqueness of fronts for degenerate diffusionconvection 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 travelingwave 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
semiwavefronts with the same speed.