Bilinear optimal control for a wave equation with viscous damping (Q2716456)
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scientific article; zbMATH DE number 1599016
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Bilinear optimal control for a wave equation with viscous damping |
scientific article; zbMATH DE number 1599016 |
Statements
16 May 2001
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necessary optimality conditions
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optimal control
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wave equation
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viscous damping
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existence
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maximum principle
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Bilinear optimal control for a wave equation with viscous damping (English)
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The paper considers an optimal control problem for the wave equation NEWLINE\[NEWLINEy_{tt}= \Delta y-k(t) y_t- q(x)y+ f,\quad (x,t)\in \Omega\times (0,T),NEWLINE\]NEWLINE with viscous damping and zero Dirichlet boundary conditions. The coefficient \(k\) plays the role of control. Under some assumptions on \(q\), \(f\) and initial conditions the differentiability of the mapping \(k\to y(k)\), the existence of an optimal control and the maximum principle are proved.
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