Global Existence and internal stabilization for a reaction-diffusion system posed on non coincident spatial domains
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 nonnega- tive 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 nonnegativity of both components. Our results apply to predator-prey systems.