Periodic optimal control for parabolic Volterra‐Lotka type equations

摘要

AbstractThis 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 withL∞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 construc