Stationary patterns of strongly coupled prey--predator models
type: Item
instance of: scholarly article
title: Stationary patterns of strongly coupled prey--predator models
zbMATH Open document ID: 1160.35325
author: Mingxin Wang
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-08-06T00:00:00Z
review text: The author considers the strongly coupled system \[ -\text{div} (K(u)\nabla u)= G(u) \quad\text{in }\Omega, \qquad \frac {\partial u}{\partial n}= 0 \quad\text{on }\partial\Omega. \tag{1} \] The author establishes a priori upper and lower bounds for positive solutions of (1), and studies the non-existence of nonconstant positive solutions. Moreover the author considers the bifurcation and the global existence with respect to diffusion terms of nonconstant positive solutions. The analysis of the author shows that the cross-diffusions may be source for the stationary patterns.
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35J55
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 2082187
zbMATH Keywords: elliptic systems
zbMATH Keywords: predator-prey models
zbMATH Keywords: cross-diffusions
zbMATH Keywords: Turing instability
zbMATH Keywords: stationary patterns
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: j.jmaa.2003.12.027
OpenAlex ID: W1997323032
Wikidata QID: Q115570469
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DOI: 10.1016/J.JMAA.2003.12.027
description: scientific article; zbMATH DE number 2082187