Limiting structure of steady-states to the Lotka-Volterra competition model with large diffusion and advection

Kousuke Kuto, Tohru Tsujikawa

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

This paper is concerned with the Neumann problem of a stationary Lotka-Volterra competition model with diffusion and advection. First we obtain some sufficient conditions of the existence of nonconstant solutions by the Leray-Schauder degree theory. Next we derive a limiting system as diffusion and advection of one of the species tend to infinity. The limiting system can be reduced to a semilinear elliptic equation with nonlocal constraint. In the simplified 1D case, the global bifurcation structure of nonconstant solutions of the limiting system can be classified depending on the coefficients. For example, this structure involves a global bifurcation curve which connects two different singularly perturbed states (boundary layer solutions and internal layer solutions). Our proof employs a levelset analysis for the associate integral mapping.

Original languageEnglish
Pages (from-to)1801-1858
Number of pages58
JournalJournal of Differential Equations
Volume258
Issue number5
DOIs
Publication statusPublished - 2015 Mar 5
Externally publishedYes

Fingerprint

Lotka-Volterra Model
Competition Model
Advection
Limiting
Global Bifurcation
Leray-Schauder Degree Theory
Internal Layers
Bifurcation Curve
Semilinear Elliptic Equations
Neumann Problem
Singularly Perturbed
Level Set
Boundary Layer
Existence of Solutions
Boundary layers
Infinity
Tend
Sufficient Conditions
Coefficient

Keywords

  • Bifurcation
  • Degree
  • Levelset analysis
  • Nonlocal constraint
  • Reaction-diffusion-advection system
  • Singular perturbation

ASJC Scopus subject areas

  • Analysis

Cite this

Limiting structure of steady-states to the Lotka-Volterra competition model with large diffusion and advection. / Kuto, Kousuke; Tsujikawa, Tohru.

In: Journal of Differential Equations, Vol. 258, No. 5, 05.03.2015, p. 1801-1858.

Research output: Contribution to journalArticle

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