### 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.

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.

#### Keywords

Competition systems; singular limits; spatial segregation

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