Optimal Control Problem for a Reaction-Diffusion System of Three Populations

Abstract

The work deals with an optimal control problem for a reaction-diffusion system comprising two competing populations, one of which is a prey for a third population. In order to maximise the total density of these populations, the existence and uniqueness of a positive strong solution of a controlled system are studied. After that, the techniques of minimal sequences is used in order to show the existence of an optimal solution. The first and second order optimality conditions are also constructed.