Asymptotic behaviour of solutions for some competition model with migration effect
type: Item
instance of: scholarly article
title: Asymptotic behaviour of solutions for some competition model with migration effect
zbMATH Open document ID: 0707.92023
author: Syozo Niizeki
author: Yuzo Hosono
published in: Journal of Mathematics of Kyoto University
publication date: 1989-01-01T00:00:00Z
review text: This paper is concerned with the study of a couple of hyperbolic equations with a growth term of Volterra-Lotka type: \[ (\partial /\partial t+\partial /\partial x)u_ 1=(1-u_ 1-b_ 1u_ 2)u_ 1,\quad (\partial /\partial t-\partial /\partial x)u_ 2=a(1-b_ 2u_ 1-u_ 2)u_ 2,\quad (x,t)\in {\mathbb{R}}\times {\mathbb{R}}_+, \] with the initial conditions: \[ (u_ 1(x,0)=u_{10}(x),\quad u_ 2(x,0)=u_{20}(x),\quad x\in {\mathbb{R}}, \] where \(u_ i(x,t)\) are the population densities of two competing species. The authors have proved the \(C_ 0\)-stability of a couple of travelling wave solutions and have studied the asymptotic behaviour of the solutions for the Cauchy problem with some class of initial data. The proofs are based on the properties of the lower and upper solutions for the Cauchy problem.
Mathematics Subject Classification ID: 92D40
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35L45
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 4162717
zbMATH Keywords: lower solution
zbMATH Keywords: growth term of Volterra-Lotka type
zbMATH Keywords: competing species
zbMATH Keywords: travelling wave solutions
zbMATH Keywords: Cauchy problem
zbMATH Keywords: upper solutions
reviewed by: Sebastian Aniţa
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250520263
OpenAlex ID: W1482157045
DOI: 10.1215/KJM/1250520263
description: scientific article; zbMATH DE number 4162717