Existence and Non-Existence of Fisher-KPP Transition Fronts
Journal Article
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 the 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. © 2011 Springer-Verlag.
Full Text
Duke Authors
Cited Authors
- Nolen, J; Roquejoffre, JM; Ryzhik, L; Zlatoš, A
Published Date
- 2012
Published In
Volume / Issue
- 203 / 1
Start / End Page
- 217 - 246
International Standard Serial Number (ISSN)
- 0003-9527
Digital Object Identifier (DOI)
- 10.1007/s00205-011-0449-4