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Uniform decay rates for the solutions to the Euler-Bernoulli plate equation with boundary feedback acting via bending moments. (English) Zbl 0754.35177

The aim of this paper is to consider a physically valid and meaningful model of the Euler-Bernoulli plate with boundary conditions. The author proves that the appropriately selected boundary feedback uniformly stabilizes the model, i.e., the energy decays to zero when \(t\to+\infty\).
The author develops new regularity results for the traces of the solution to special types of plates problems. This regularity together with sharp energy estimates imply that uniform stabilization holds.
Reviewer: S.Anita (Iaşi)

MSC:

35Q72 Other PDE from mechanics (MSC2000)
93D15 Stabilization of systems by feedback
35B37 PDE in connection with control problems (MSC2000)
74K20 Plates
35B65 Smoothness and regularity of solutions to PDEs