PERIODIC OPTIMAL-CONTROL FOR PARABOLIC VOLTERRA-LOTKA TYPE EQUATIONS

This paper considers the optimal harvesting control of a biological species, whose growth is governed by the parabolic diffusive Volterra-Lotka equation. We prove that such equation with Lm periodic coefficients has an unique positive periodic solution. We show the existence and uniqueness of an optimal control, and under certain conditions, we characterize the optimal control in terms of a parabolic optimality system. A monotone sequence which converges to the optimal control is constructed.