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; ZlatoŇ°, 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