Boundary stabilization for the wave equation in a bounded cylindrical domain

Kim Dang Phung

doi:10.3934/dcds.2008.20.1057

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2008, Volume 20, Issue 4: 1057-1093. Doi: 10.3934/dcds.2008.20.1057

This issue Previous Article Viscosity solutions of fully nonlinear second order parabolic equations with $L^1$ dependence in time and Neumann boundary conditions. Existence and applications to the level-set approach Next Article Rotation numbers and Lyapunov stability of elliptic periodic solutions

Boundary stabilization for the wave equation in a bounded cylindrical domain

Kim Dang Phung^1,

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

Received: January 2007

Revised: October 2007

Published: October 2008

Abstract / Introduction Related Papers Cited by

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.

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