Competition in periodic media: III -- Existence & stability of segregated periodic coexistence states

Léo Girardin (1) , Alessandro Zilio (1)

1 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions

In this paper we consider a system of parabolic reaction-diffusion equations with strong competition and two related scalar reaction-diffusion equations. We are mainly concerned with the case of periodic coefficients and periodic solutions. We show that, for sufficiently large periods, these models have stationary, non-constant, fully non-trivial and stable solutions. We compare our results with already known results about the existence and non-existence of such solutions. Finally, we provide ecological interpretations for these results in terms of resistance against an invasion.

Mots clés: segregation; stability; Competition--diffusion system; periodic media

Domaines: Equations aux dérivées partielles [math.AP]

Léo Girardin, Alessandro Zilio. Competition in periodic media: III -- Existence & stability of segregated periodic coexistence states. 2019. ⟨hal-01717542v4⟩