# American Institute of Mathematical Sciences

October  2008, 20(4): 1057-1093. doi: 10.3934/dcds.2008.20.1057

## Boundary stabilization for the wave equation in a bounded cylindrical domain

 1 Yangtze Center of Mathematics, Sichuan University, Chengdu 610064, China

Received  January 2007 Revised  October 2007 Published  January 2008

We provide a polynomial decay rate for the energy of the wave equation with a dissipative boundary condition in a cylindrical trapped domain. A new kind of interpolation estimate for the wave equation with mixed Dirichlet-Neumann boundary condition is established from a construction based on a Fourier integral operator involving a good choice of weight functions.
Citation: Kim Dang Phung. Boundary stabilization for the wave equation in a bounded cylindrical domain. Discrete & Continuous Dynamical Systems - A, 2008, 20 (4) : 1057-1093. doi: 10.3934/dcds.2008.20.1057
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