Topological Methods in Nonlinear Analysis

Competition systems with strong interaction on a subdomain

Elaine C.M. Crooks and E. Norman Dancer

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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.

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Topol. Methods Nonlinear Anal., Volume 37, Number 1 (2011), 37-53.

First available in Project Euclid: 20 April 2016

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Crooks, Elaine C.M.; Dancer, E. Norman. Competition systems with strong interaction on a subdomain. Topol. Methods Nonlinear Anal. 37 (2011), no. 1, 37--53.

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