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arXiv · 2109.01521

Stabilization of the damped plate equation under general boundary conditions

Jérôme Le Rousseau·Emmanuel Wend-Benedo Zongo
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Abstract

We consider a damped plate equation on an open bounded subset of R^d, or a smooth manifold, with boundary, along with general boundary operators fulfilling the Lopatinskii-Sapiro condition. The damping term acts on a region without imposing a geometrical condition. We derive a resolvent estimate for the generator of the damped plate semigroup that yields a logarithmic decay of the energy of the solution to the plate equation. The resolvent estimate is a consequence of a Carleman inequality obtained for the bi-Laplace operator involving a spectral parameter under the considered boundary conditions. The derivation goes first though microlocal estimates, then local estimates, and finally a global estimate.

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Jérôme Le Rousseau, Emmanuel Wend-Benedo Zongo. 2021-09-06. Stabilization of the damped plate equation under general boundary conditions. https://arxiv.org/abs/2109.01521

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