Regional optimal control approach for a spatiotemporal prey-predator model

Abstract

In this paper, we consider a spatiotemporal Prey-Predator system with a diffusion term. Our main objective is to characterize the two optimal controls that minimize the density of prey population also to minimize the density of the predator population to reach the ecological balance in two imposed different regions ω₁ and ω₂ (it is not excluded that ω₁=ω₂). For that reason we prove the existence of a pair of control and provide a characterization of optimal control in term of state and adjoint function. Finally, we present numerical simulation to justify our main results and to support the theoretical conclusions.