Nearly a polynomial decay rate for the dissipative wave equation
نویسنده
چکیده
The study of stabilization of the linear dissipative wave equation in a bounded domain with Dirichlet boundary condition is now an old problem. The exponential decay rate of the energy was established by Bardos, Lebeau and Rauch [ BLR] 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 [ L] proved a logarithmic decay rate for smooth solutions when no particular geometric condition is required. The goal of this paper is to present a better decay estimate than the logarithmic one when the geometric control condition is not fulfilled. Our main result is:
منابع مشابه
Polynomial decay rate for the dissipative wave equation
This paper is devoted to study the stabilization of the linear wave equation in a bounded domain damped in a subdomain when the geometrical control condition (see [ BLR]) of the work of C. Bardos, G. Lebeau and J. Rauch is not fulfilled. In such case, they [ BLR] proved that the uniform exponential decay rate of the energy cannot be hoped due to the existence of a trapped ray that never reaches...
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