Competition systems with strong interaction on a subdomain

Elaine C. M. Crooks, E. Norman Dancer


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.


Competition systems; singular limits; spatial segregation

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