Existence and Non-existence of Fisher-KPP Transition Fronts

Details Existence and Non-existence of Fisher-KPP Transition Fronts Existence and Non-existence of Fisher-KPP Transition Fronts

2010-12-10

arxiv.org/abs/1012.2392v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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