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

Domaines: Equations aux dérivées partielles [math.AP]

Léo Girardin. Non-cooperative Fisher–KPP systems: asymptotic behavior of traveling waves. Mathematical Models and Methods in Applied Sciences, 2018, 28 (06), pp.1067-1104. ⟨hal-01569486v3⟩