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June  2009, 11(4): 805-822. doi: 10.3934/dcdsb.2009.11.805

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

Sebastian Aniţa 1, , William Edward Fitzgibbon 2, and  Michel Langlais 3,

1. 

Faculty of Mathematics, University “Al.I. Cuza” and, Institute of Mathematics “Octav Mayer”, Iaşi 700506
2. 

Departments of Engineering Technology and Mathematics, University of Houston, Houston, Texas 77204-3476, United States
3. 

Université Victor Segalen Bordeaux 2, case 26, UMR CNRS 5251 IMB & INRIA Futurs Anubis, 146, rue Léo Saignat, 33076 Bordeaux Cedex

Received  June 2008 Revised  September 2008 Published  April 2009

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: predator-prey model., stabilization, non coincident spatial domains, Reaction-diffusion systems, principal eigenvalue, global existence.
Mathematics Subject Classification: Primary: 35K57, 35P05, 93C20, 92D25; Secondary: 35B3.
Citation: Sebastian Aniţa, William Edward Fitzgibbon, Michel Langlais. Global existence and internal stabilization for a reaction-diffusion system posed on non coincident spatial domains. Discrete and Continuous Dynamical Systems - B, 2009, 11 (4) : 805-822. doi: 10.3934/dcdsb.2009.11.805
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