  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.
