Stabilization of the damped plate equation under general boundary conditions
Analysis of PDEs
2021-09-07 v2 Functional Analysis
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.
Keywords
Cite
@article{arxiv.2109.01521,
title = {Stabilization of the damped plate equation under general boundary conditions},
author = {Jérôme Le Rousseau and Emmanuel Wend-Benedo Zongo},
journal= {arXiv preprint arXiv:2109.01521},
year = {2021}
}