Limiting characterization of stationary solutions for a prey-predator model with nonlinear diffusion of fractional type

Kousuke Kuto, Yoshio Yamada

研究成果: Article査読

7 被引用数 (Scopus)

抄録

We consider the following quasilinear elliptic system: (EQUATION PRESENT) where Ω is a bounded domain in ℝ. This system is a stationary problem of a prey-predator model with non-linear diffusion δ(v/ 1+βu ), and u (respectively v) denotes the population density of the prey (respectively the predator). Kuto [15] has studied this system for large β under the restriction b > (1 + γ)λ1, where λ1 is the least eigenvalue of -δ with homogeneous Dirichlet boundary condition. The present paper studies two shadow systems and gives the complete limiting characterization of positive solutions as β → ∞ without any restriction on b.

本文言語English
ページ(範囲)725-752
ページ数28
ジャーナルDifferential and Integral Equations
22
7-8
出版ステータスPublished - 2009 7 1
外部発表はい

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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