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Optimal boundary control of hyperbolic equations with pointwise state constraints. (English) Zbl 1153.49315

Summary: We consider dynamic optimization problems for hyperbolic systems with boundary controls and pointwise state constraints. In contrast to parabolic dynamics, such systems have not been sufficiently studied in the literature. The reason is the lack of regularity in the case of hyperbolic dynamics. We present necessary optimality conditions for both Neumann and Dirichlet boundary control problems and discuss differences and relationships between them.

MSC:

49K40 Sensitivity, stability, well-posedness
35L20 Initial-boundary value problems for second-order hyperbolic equations
49J52 Nonsmooth analysis
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References:

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