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Optimal shape and position of the support for the internal exact control of a string. (English) Zbl 1155.49312
Summary: We consider the problem of optimizing the shape and position of the support ω of the internal exact control of minimal L 2 (0,T;L 2 (ω))-norm for the 1-D wave equation. A relaxation for this problem is found and the minimizers of the relaxed problem are characterized through first-order optimality conditions.
49Q20Variational problems in a geometric measure-theoretic setting
70Q05Control of mechanical systems (general mechanics)
74K05Strings (solid mechanics)
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