A 3-component system of competition and diffusion
type: Item
instance of: scholarly article
title: A 3-component system of competition and diffusion
zbMATH Open document ID: 0615.92016
author: Masayasu Mimura
author: Paul C. Fife
published in: Hiroshima Mathematical Journal
publication date: 1986-01-01T00:00:00Z
review text: The authors discuss the existence of non-constant steady states of a system of the form \[ \frac{\partial u_ i}{\partial t}=d_ i\frac{\partial^ 2u_ i}{\partial x^ 2}+(r_ i- \sum^{N}_{j=1}a_{ij}u_ j)u_ i,\quad x\in (0,1),\quad t\in (0,\infty),\quad i=1,...,N, \] subject to von Neumann boundary conditions, where \(d_ i\), \(r_ i\) and \(a_{ij}\) are nonnegative constants. In particular they consider the case \(N=3.\) Using singular perturbation techniques they show that under certain conditions non constant solutions may exist.
Mathematics Subject Classification ID: 92D40
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 35K50
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 3997604
zbMATH Keywords: competition
zbMATH Keywords: diffusion
zbMATH Keywords: two-point boundary value problems
zbMATH Keywords: 3-component systems
zbMATH Keywords: spatially dispersing species
zbMATH Keywords: spatial segregation
zbMATH Keywords: reaction- diffusion equations
zbMATH Keywords: existence of non-constant steady states
zbMATH Keywords: von Neumann boundary conditions
zbMATH Keywords: non constant solutions
reviewed by: Robert L. Taylor
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3997604