Optimal Control for Degenerate Parabolic Equations
نویسندگان
چکیده
This paper considers the optimal control of a degenerate parabolic partial differential equation governing a di usive population with logistic growth terms. Assuming this population causes damage to forest and agricultural land, the optimal control is the trapping rate and the cost functional is a combination of the damage and trapping costs. We prove existence, uniqueness, and regularity results for this degenerate parabolic equation. The vanishing viscosity method is used to obtain the existence result. The optimal control is characterized in terms of the solution of the optimality system, which is the state equation coupled with the adjoint equation. Uniqueness for the solutions of the optimality system is valid for a su ciently small time interval due to the opposite time orientations of the two equations involved.
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