Uniqueness and nonuniqueness of fronts for degenerate diffusion-convection reaction equations
Analysis of PDEs
2020-08-11 v2
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.
Keywords
Cite
@article{arxiv.2007.02892,
title = {Uniqueness and nonuniqueness of fronts for degenerate diffusion-convection reaction equations},
author = {Diego Berti and Andrea Corli and Luisa Malaguti},
journal= {arXiv preprint arXiv:2007.02892},
year = {2020}
}
Comments
35 pages, 10 figures; submitted version. Revision with exposition changes, typos fixed and assumption (6.3) added to Propositions 6.1 and 8.2