Stabilization of the wave equation with moving boundary

Kaïs Ammari; Ahmed Bchatnia; Karim El Mufti

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arXiv · 1705.01622

Stabilization of the wave equation with moving boundary

Kaïs Ammari·Ahmed Bchatnia·Karim El Mufti

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Abstract

We deal with the wave equation with assigned moving boundary ($0<x<a(t)$) upon which Dirichlet-Neuman boundary conditions are satisfied, here $a(t)$ is assumed to move slower than the light and periodically. We give a feedback which guarantees the exponential decay of the energy. The proof relies on a reduction theorem of Yoccoz. At the end we give a remark on the moving-pointwise stabilization problem.

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Kaïs Ammari, Ahmed Bchatnia, Karim El Mufti. 2017-05-03. Stabilization of the wave equation with moving boundary. https://arxiv.org/abs/1705.01622

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