Competition systems with strong interaction on a subdomain
Elaine Crooks, Edward Norman Dancer · Project Euclid (Cornell University) · 2011
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.