Optimal harvesting-coefficient control of steady-state prey-predator diffusive Volterra-Lotka systems

Abstract

This article considers the optimal control of the harvesting of a prey-predator system in an environment. The species are assumed to be in steady state under diffusion and Voterra-Lotka type of interaction. They are harvested for economic profit, leading to reduction of growth rates; and the problem is to control the spatial distributions of harvests so as to optimize the return. Precise conditions are found so that the optimal control can be rigorously characterized as the solution of an optimality system of nonlinear elliptic partial differential equations. Moreover, a constructive approximation scheme for optimal control is given.