Boundary stabilization for the wave equation in a bounded cylindrical domain

Pages: 1057 - 1093, Volume 20, Issue 4, April 2008

doi:10.3934/dcds.2008.20.1057       Abstract        Full Text (334.5K)       Related Articles

Kim Dang Phung - Yangtze Center of Mathematics, Sichuan University, Chengdu 610064, China (email)

Abstract: 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.

Keywords:  Wave equation, Mixed Dirichlet-Neumann boundary condition, Polynomial energy decay rate.
Mathematics Subject Classification:  Primary: 35L05, 35S30; Secondary: 49J20.

Received: January 2007;      Revised: October 2007;      Published: January 2008.