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Zbl 1211.49032
Criado-Aldeanueva, F.; Criado, F.; Odishelidze, N.; Sanchez, J.M.
On a control problem governed by a linear partial differential equation with a smooth functional. (English)
[J] Optim. Control Appl. Methods 31, No. 6, 497-503 (2010). ISSN 0143-2087

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 2000:: *49K20 Optimal control problems with PDE (nec./ suff.)
35J25 Second order elliptic equations, boundary value problems
35Q93

Keywords: Helmholtz equation; boundary value problems; optimality for control problems

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