GLOBAL EXISTENCE AND INTERNAL STABILIZATION FOR A REACTION-DIFFUSION SYSTEM POSED ON NON COINCIDENT SPATIAL DOMAINS

We consider a two-component Reaction-Diffusion system posed on non coincident spatial domains and featuring are action term involving an integral kernel. The question of global existence of component wise non negative solutions is assessed. Then we investigate the stabilization of one of the solution components to zero via an internal control distributed on a small sub domain while preserving non negativity of both components. Our results apply to predator-prey systems.