Boundary stabilization of Venttsel problems (Q2701816)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Boundary stabilization of Venttsel problems |
scientific article |
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5 March 2001
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elastodynamic systems
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wave equation
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Venttsel problem
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nonlinear boundary feedback
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boundary stabilization
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energy decay rates
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exponential decay
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Boundary stabilization of Venttsel problems (English)
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The author gives results on boundary stabilization for elastodynamic systems with Venttsel conditions. In the case of stationary Venttsel conditions, a nonlinear boundary feedback implies an energy decay to zero. The invariance principle of LaSalle is a main tool. For evolutive Venttsel conditions, a suitable boundary feedback leads to arbitrarily large energy decay rates. It is based on a general method developed by \textit{V. Komornik} [C. R. Acad. Sci., Paris, Sér. I, 321, No. 5, 581-586 (1995; Zbl 0872.93071)]. Finally, by a spectral study, the author proves that the natural feedback does not assure exponential decay for the wave equation with Venttsel conditions.
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