Energy decay rates for solutions of the wave equation with linear damping in exterior domain

Details Energy decay rates for solutions of the wave equation with linear damping in exterior domain Energy decay rates for solutions of the wave equation with linear damping in exterior domain

2012-03-30

arxiv.org/abs/1203.6780v2

Mathematics

Optimization and Control

18 pages

Scientific paper

In this paper we study the behavior of the energy of solutions of the wave equation with localized damping in exterior domain. We assume that the damper is positive at infinity. Under the Geometric Control Condition of Bardos et al (1992), we prove that: 1) The total energy decay like O(1/t) and L^2-norm is bounded for the solutions with initial data in (H_0^1,L^2). 2) The total energy and the square of the L^2-norm, repectively, decay like O(1/t^2) and O(1/t) for a kind of the weighted initial data.

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