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Discrete and Continuous Dynamical Systems - Series B (DCDS-B)
 

Global existence and internal stabilization for a reaction-diffusion system posed on non coincident spatial domains

Pages: 805 - 822, Volume 11, Issue 4, June 2009      doi:10.3934/dcdsb.2009.11.805

 
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Sebastian Aniţa - Faculty of Mathematics, University “Al.I. Cuza” and, Institute of Mathematics “Octav Mayer”, Iaşi 700506, Romania (email)
William Edward Fitzgibbon - Departments of Engineering Technology and Mathematics, University of Houston, Houston, Texas 77204-3476, United States (email)
Michel Langlais - Université Victor Segalen Bordeaux 2, case 26, UMR CNRS 5251 IMB & INRIA Futurs Anubis, 146, rue Léo Saignat, 33076 Bordeaux Cedex, France (email)

Abstract: We consider a two-component Reaction-Diffusion system posed on non coincident spatial domains and featuring a reaction term involving an integral kernel. The question of global existence of componentwise nonnegative solutions is assessed. Then we investigate the stabilization of one of the solution components to zero via an internal control distributed on a small subdomain while preserving nonnegativity of both components. Our results apply to predator-prey systems.

Keywords:  Reaction-diffusion systems, non coincident spatial domains, global existence, stabilization, principal eigenvalue, predator-prey model.
Mathematics Subject Classification:  Primary: 35K57, 35P05, 93C20, 92D25; Secondary: 35B37.

Received: June 2008;      Revised: September 2008;      Available Online: April 2009.