Competition systems with strong interaction on a subdomain

Abstract

We study the large-interaction limit of an elliptic system modelling the steady states of two species $u$ and $v$ which compete to some extent throughout a domain $\Omega$ but compete strongly on a subdomain $A \subset \Omega$. In the strong-competition limit, $u$ and $v$ segregate on $A$ but not necessarily on $\Omega \setminus A$. The limit problem is a system on $\Omega \setminus A$ and a scalar equation on $A$ and in general admits an interesting range of types of solution, not all of which can be the strong-competition limit of coexistence states of the original system.