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.
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 |