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

2016/12/17 by Léo Girardin, Girardin, Léo · 1 citation
Engineering · Mathematics · Medicine · #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models #Stability and Controllability of Differential Equations

paper · doi:10.48550/arxiv.1612.05774

openalex publication_date 2016/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Planar pulsating traveling wave solutions of non-cooperative Fisher--KPP systems in space-time periodic media

Related

• Non-cooperative Fisher--KPP systems: asymptotic behavior of traveling waves
• A Liouville-type result for non-cooperative Fisher--KPP systems and nonlocal equations in cylinders
• Travelling waves in the Fisher-KPP equation with nonlinear diffusion and a non-Lipschitzian reaction term
• Semi-wave, traveling wave and spreading speed for monostable cooperative systems with nonlocal diffusion and free boundaries
• Planar pulsating traveling wave solutions of non-cooperative Fisher--KPP systems in space-time periodic media