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Influence of the hidden regularity on the stability of partially damped systems of wave equations. (English. French summary) Zbl 1451.93292

Summary: We consider the stability of a system of two wave equations with only one boundary feedback and we show that the stability of the partially damped system depends on the transmission of energy between the two equations. The study confirms that the hidden regularity is an essential ingredient for the stability property. In particular, using a sharp regularity for Neumann problem of wave equation, we improve the usual results on the energy decay rate. This new approach can certainly be applied to other situations of partially damped systems.

MSC:

93D15 Stabilization of systems by feedback
93C20 Control/observation systems governed by partial differential equations
35L05 Wave equation
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