Exponential stabilization of waves for the Zaremba boundary condition
Abstract
In this article we prove, under some geometrical condition on geodesic flow, exponential stabilization of wave equation with Zaremba boundary condition. We prove an estimate on the resolvent of semigroup associated with wave equation on the imaginary axis and we deduce the stabilization result. To prove this estimate we apply semiclassical measure technics. The main difficulties are to prove that support of measure is in characteristic set in a neighborhood of the jump in the boundary condition and to prove results of propagation in a neighborhood of a boundary point where Neumann boundary condition is imposed. In fact if a lot of results applied here are proved in previous articles, these two points are new.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.05986
 Bibcode:
 2021arXiv211005986C
 Keywords:

 Mathematics  Analysis of PDEs