Non-cooperative Fisher–KPP systems: asymptotic behavior of traveling waves

Léo Girardin (1)

1 LJLL - Laboratoire Jacques-Louis Lions

This paper is concerned with non-cooperative parabolic reaction–diffusion systems which share structural similarities with the scalar Fisher–KPP equation. In a previous paper, we established that these systems admit traveling wave solutions. It is then natural to investigate their asymptotic distributions. This is the main object of this paper. Non-cooperative KPP systems can model various phenomena where the following three mechanisms occur: local diffusion in space, linear cooperation and superlinear competition.

Mots clés: KPP nonlinearities; reaction–diffusion system; steady states; structured population; traveling waves.

Domaines: Equations aux dérivées partielles [math.AP]

Léo Girardin. Non-cooperative Fisher–KPP systems: asymptotic behavior of traveling waves. 2017. ⟨hal-01569486v2⟩