Nonconvex optimal control of nonlinear monotone parabolic systems (Q1083682)

An optimal control problem is studied for distributed systems governed by nonlinear parabolic PDE's with state constraints. The state equation is monotone in the state variable and nonlinear in the control variable. The constraints and the cost functional are not necessarily convex. Relaxed controls are used to prove the existence of an optimal control. Moreover, a minimum principle of relaxed optimality of Pontryagin type is established. The relaxation technique can also be used to develope numerical methods for solving nonconvex optimal control problems of systems defined by PDE's.