Diffusion-convection reaction equations with sign-changing diffusivity and bistable reaction term
Analysis of PDEs
2021-07-23 v1
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.
Cite
@article{arxiv.2107.10530,
title = {Diffusion-convection reaction equations with sign-changing diffusivity and bistable reaction term},
author = {Diego Berti and Andrea Corli and Luisa Malaguti},
journal= {arXiv preprint arXiv:2107.10530},
year = {2021}
}
Comments
33 pages, 8 figures