Global existence and internal stabilization for a reaction-diffusion system posed on non coincident spatial domains
The authors consider a two-component reaction-diffusion system posed on non coincident spatial domains and featuring a reaction term involving an integral kernel. Global existence results for nonnegative componentwise solutions to the resulting initial value and no-flux boundary conditions problem are obtained, together with a global stability result for a semi trivial stationary state corresponding to the extinction of predators. Then it is studied the large time stabilization of one of the solution components toward zero while preventing the second component going to zero. This is achieved via internal controls distributed on a small subdomain preserving the nonnegativity of both components. The results are applyed to predator-prey systems.
scientific article; zbMATH DE number 5574123