Optimal resource control in reaction diffusion advection population model

Abstract

This paper is to investigate the control problem of maximizing the net benefit of a single species while the cost of the resource allocation is minimized in a population model which can be described by a reaction diffusion advection equation of logistic type with spatial-temporal resource control coefficient. The existence of an optimal control is established and the uniqueness and characterization of the optimal control are investigated. Numerical simulation illustrate several cases with Dirichlet and Neumann boundary conditions.