Convergence to a terrace solution in multistable reaction-diffusion equations with discontinuities
Analysis of PDEs
2022-08-01 v1
Abstract
In this paper we address the large-time behavior of solutions of bistable and multistable reaction-diffusion equations with discontinuities around the stable steady states. We show that the solution always converges to a special solution, which may either be a traveling wave in the bistable case, or more generally a terrace (i.e. a collection of stacked traveling waves with ordered speeds) in the multistable case.
Cite
@article{arxiv.2207.14565,
title = {Convergence to a terrace solution in multistable reaction-diffusion equations with discontinuities},
author = {Thomas Giletti and Ho-Youn Kim},
journal= {arXiv preprint arXiv:2207.14565},
year = {2022}
}