Sebastian Aniţa - Faculty of Mathematics, University “Al.I. Cuza” and, Institute of Mathematics “Octav Mayer”, Iaşi 700506, Romania (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.
Received: June 2008; Revised: September 2008; Published: April 2009.
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