  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.
