Global existence and internal stabilization for a reaction-diffusion system posed on non coincident spatial domains
type: Item
instance of: scholarly article
title: Global existence and internal stabilization for a reaction-diffusion system posed on non coincident spatial domains
zbMATH Open document ID: 1178.35055
author: Sebastian Aniţa
author: W. E. Fitzgibbon
author: M. Langlais
published in: Discrete and Continuous Dynamical Systems. Series B
publication date: 2009-07-02T00:00:00Z
review text: The authors consider a two-component reaction-diffusion system posed on non coincident spatial domains and featuring a reaction term involving an integral kernel. Global existence results for nonnegative componentwise solutions to the resulting initial value and no-flux boundary conditions problem are obtained, together with a global stability result for a semi trivial stationary state corresponding to the extinction of predators. Then it is studied the large time stabilization of one of the solution components toward zero while preventing the second component going to zero. This is achieved via internal controls distributed on a small subdomain preserving the nonnegativity of both components. The results are applyed to predator-prey systems.
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35P05
Mathematics Subject Classification ID: 93C20
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 35R09
zbMATH DE Number: 5574123
zbMATH Keywords: principal eigenvalue
zbMATH Keywords: predator-prey model
zbMATH Keywords: no-flux boundary conditions
reviewed by: Lubomira Softova
MaRDI profile type: Publication
full work available at URL: dcdsb.2009.11.805
OpenAlex ID: W1970172819
DOI: 10.3934/DCDSB.2009.11.805
description: scientific article; zbMATH DE number 5574123