Pulsating solutions for multidimensional bistable and multistable equations
Analysis of PDEs
2019-01-23 v1
Abstract
We devote this paper to the issue of existence of pulsating travelling front solutions for spatially periodic heterogeneous reaction-diffusion equations in arbitrary dimension, in both bistable and more general multistable frameworks. In the multistable case, the notion of a single front is not sufficient to understand the dynamics of solutions, and we instead observe the appearance of a so-called propagating terrace. This roughly refers to a finite family of stacked fronts connecting intermediate stable steady states whose speeds are ordered. Surprisingly, for a given equation, the shape of this terrace (i.e., the involved intermediate states or even the cardinality of the family of fronts) may depend on the direction of propagation.
Cite
@article{arxiv.1901.07256,
title = {Pulsating solutions for multidimensional bistable and multistable equations},
author = {Thomas Giletti and Luca Rossi},
journal= {arXiv preprint arXiv:1901.07256},
year = {2019}
}