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arXiv · 1612.05774

Non-cooperative Fisher--KPP systems: traveling waves and long-time behavior

Léo Girardin
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Abstract

This paper is concerned with non-cooperative parabolic reaction--diffusion systems which share structural similarities with the scalar Fisher--KPP equation. These similarities make it possible to prove, among other results, an extinction and persistence dichotomy and, when persistence occurs, the existence of a positive steady state, the existence of traveling waves with a half-line of possible speeds and a positive minimal speed and the equality between this minimal speed and the spreading speed for the Cauchy problem. Non-cooperative KPP systems can model various phenomena where the following three mechanisms occur: local diffusion in space, linear cooperation and su-perlinear competition.

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Léo Girardin. 2016-12-17. Non-cooperative Fisher--KPP systems: traveling waves and long-time behavior. https://arxiv.org/abs/1612.05774

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