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Implications of sharp trace regularity results on boundary stabilization of the system of linear elasticity. (English) Zbl 0913.93062

The purpose of this very important paper is the study of a question concerning the problem of uniform-exponential decay of solutions to the elastodynamic system of elasticity using boundary feedback control. Energy dissipation is introduced via linear velocity feedbacks acting through a portion of the boundary as traction forces. Two primary goals are achieved: First, these results are proven without the imposition of strong geometric assumptions on the controlled portion of the boundary (thus extending earlier work which required that the domain should be star shaped). Second, the feedback is only a function of velocity (as opposed to the previous one also containing the tangential derivative of the displacement), resulting in a physically viable feedback. The proof of the main result is based on the multiplier method and relies critically on sharp trace estimates for the tangential derivative of the displacement on the boundary as well as on unique continuation results for the corresponding static system.

MSC:

93D15 Stabilization of systems by feedback
93C20 Control/observation systems governed by partial differential equations
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