Existence and Non-existence of Fisher-KPP Transition Fronts
Analysis of PDEs
2015-05-20 v1
Abstract
We consider Fisher-KPP-type reaction-diffusion equations with spatially inhomogeneous reaction rates. We show that a sufficiently strong localized inhomogeneity may prevent existence of transition-front-type global in time solutions while creating a global in time bump-like solution. This is the first example of a medium in which no reaction-diffusion transition front exists. A weaker localized inhomogeneity leads to existence of transition fronts but only in a finite range of speeds. These results are in contrast with both Fisher-KPP reactions in homogeneous media as well as ignition-type reactions in inhomogeneous media.
Keywords
Cite
@article{arxiv.1012.2392,
title = {Existence and Non-existence of Fisher-KPP Transition Fronts},
author = {James Nolen and Jean-Michel Roquejoffre and Lenya Ryzhik and Andrej Zlatos},
journal= {arXiv preprint arXiv:1012.2392},
year = {2015}
}