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Boundary stabilization of Venttsel problems. (Stabilisation frontière de problèmes de Ventcel.) (French) Zbl 0967.93048

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 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.
Reviewer: O.Cârjá (Iaşi)

MSC:

93C20 Control/observation systems governed by partial differential equations
93D15 Stabilization of systems by feedback
74M05 Control, switches and devices (“smart materials”) in solid mechanics

Citations:

Zbl 0872.93071
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References:

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