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

Kousuke Kuto, Yoshio Yamada

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)725-752
Number of pages28
JournalDifferential and Integral Equations
Volume22
Issue number7-8
Publication statusPublished - 2009 Jul
Externally publishedYes

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Prey-predator Model
Nonlinear Diffusion
Stationary Solutions
Fractional
Limiting
Boundary conditions
Least Eigenvalue
Restriction
Quasilinear Elliptic Systems
Predator
Prey
Dirichlet Boundary Conditions
Positive Solution
Bounded Domain
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ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Limiting characterization of stationary solutions for a prey-predator model with nonlinear diffusion of fractional type. / Kuto, Kousuke; Yamada, Yoshio.

In: Differential and Integral Equations, Vol. 22, No. 7-8, 07.2009, p. 725-752.

Research output: Contribution to journalArticle

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