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On a control problem governed by a linear partial differential equation with a smooth functional. (English) Zbl 1211.49032
Summary: The optimal control problem for the Helmholtz equation with non-local boundary conditions is considered. Necessary and sufficient conditions of optimality in a maximum principle form have been obtained. We note that this problem is basically different from classical-type problems because it is impossible to use Green’s formula and we cannot rewrite it in the variational form widely used in the literature. So it is impossible to use all the theory that has been developed for optimal control problems with classical boundary conditions.
MSC:
49K20Optimal control problems with PDE (optimality conditions)
35J25Second order elliptic equations, boundary value problems
35Q93PDEs in connection with control and optimization