Polynomial decay rate for the dissipative wave equation

Details Polynomial decay rate for the dissipative wave equation Polynomial decay rate for the dissipative wave equation

2003-12-15

arxiv.org/abs/math/0312281v2

Mathematics

Analysis of PDEs

18 pages. Major changes and improvements

Scientific paper

We study the dissipative linear wave equation in a bounded domain. The exponential decay rate of the energy was established by Bardos, Lebeau and Rauch under a geometrical hypothesis linked with the geodesics. Furthermore such condition called geometric control condition is almost necessary to get a uniform exponential decay. In another hand, Lebeau proved a logarithmic decay rate for smooth solutions when no particular geometric condition is required. In this paper we give for some particular geometries a polynomial decay rate when the geometric control condition is not fulfilled.

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