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Competing species equations with diffusion, large interactions, and jumping nonlinearities. (English) Zbl 0815.35024

In this paper a reaction-diffusion system of the form \[ - \Delta u = au - u^ 2 - cuv, \quad - \Delta u = dv - v^ 2 - euv \quad \text{in} \quad D \subset \mathbb{R}^ n \] with homogeneous Dirichlet boundary conditions is studied. \(a,c,d,e\) are positive constants. The authors study the asymptotic behavior of the positive solution as the parameters \(c,e\) tend to infinity.
Reviewer: R.Sperb (Zürich)

MSC:

35J65 Nonlinear boundary value problems for linear elliptic equations
35B40 Asymptotic behavior of solutions to PDEs
35K57 Reaction-diffusion equations
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
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