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

2012/03/30 by M. Daoulatli, Daoulatli, M.
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #FOS: Mathematics #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1203.6780

openalex publication_date 2012/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 L²-norm is bounded for the solutions with initial data in (H₀¹,L²). 2) The total energy and the square of the L²-norm, repectively, decay like O(1/t²) and O(1/t) for a kind of the weighted initial data.

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