Singular limit of a competition-diffusion system with large interspecific interaction

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:390

Article

Hilhorst, Danielle¹  Martin, Sebastien¹  Mimura, Masayasu² 

[1] Univ Paris 11, Math Lab, CNRS, Fac Sci Orsay,UMR 8628, F-91405 Orsay, France

[2] Meiji Univ, Dept Math, Sch Sci & Technol, Inst Adv Studies Math Sci,Tama Ku, Kawasaki, Kanagawa, Japan

关键词: Competition-diffusion system;    Singular limit problem;    Spatial segregation;    Free boundary problem;   

DOI  :  10.1016/j.jmaa.2012.02.001

来源: Elsevier

【 摘 要 】

We consider a competition-diffusion system for two competing species; the density of the first species satisfies a parabolic equation together with an inhomogeneous Dirichlet boundary condition whereas the second one either satisfies a parabolic equation with a homogeneous Neumann boundary condition, or an ordinary differential equation. Under the situation where the two species spatially segregate as the interspecific competition rate becomes large, we show that the resulting limit problem turns out to be a free boundary problem. We focus on the singular limit of the interspecific reaction term, which involves a measure located on the free boundary. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free