Positive solutions for Lotka-Volterra competition systems with large cross-diffusion

Kousuke Kuto, Yoshio Yamada

研究成果: Article査読

30 被引用数 (Scopus)

抄録

This paper discusses the stationary problem for the Lotka-Volterra competition systems with cross-diffusion under homogeneous Dirichlet boundary conditions. Although some sufficient conditions for the existence of positive solutions are known, the information for their structure is far from complete. In order to get better understanding of the competition system with cross-diffusion, we study the effects of large cross-diffusion on the structure of positive solutions and focus on the limiting behaviour of positive solutions by letting one of the cross-diffusion coefficients to infinity. Especially, it will be shown that positive solutions of the competition system converge to a positive solution of a suitable limiting system. We will also derive some satisfactory results on positive solutions for this limiting system. These results give us important information on the structure of positive solutions for the competition system when one of the cross-diffusion coefficients is sufficiently large.

本文言語English
ページ(範囲)1037-1066
ページ数30
ジャーナルApplicable Analysis
89
7
DOI
出版ステータスPublished - 2010 7
外部発表はい

ASJC Scopus subject areas

  • 分析
  • 応用数学

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