The wave equation with a boundary control at both endpoints and the complete vibration damping problem (Q2704015)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The wave equation with a boundary control at both endpoints and the complete vibration damping problem |
scientific article |
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6 January 2002
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state with prescribed displacement and velocity
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The wave equation with a boundary control at both endpoints and the complete vibration damping problem (English)
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The authors consider the one-dimensional wave equation \(u_{tt}-u_{xx}=0\) describing the vibrations of a string with endpoints at \(x=0\) and \(x=\ell.\) At the initial time, the points of the string are given with an arbitrary displacement and an arbitrary velocity. It is studied the problem of finding the boundary controls bringing the string in finite time \(T\) to a state with prescribed displacement and velocity.
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