Differential and Integral Equations

Stabilization of the total energy for a system of elasticity with localized dissipation

María Angélica Astaburuaga and Ruy Coimbra Charão

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Abstract

In this paper we study the system of elastic waves in a bounded domain in ${{\mathbb R}}^3$ with a localized dissipation given by a function $q(x)$ in $L^r(\Omega )$. The dissipation is effective only on a neighborhood of part of the boundary of the domain. We prove algebraic decay rate of energy. In order to obtain this result we develop new energy identities for this system. Our result extend previous results for the system of elasticity and wave equation.

Article information

Source
Differential Integral Equations, Volume 15, Number 11 (2002), 1357-1376.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060727

Mathematical Reviews number (MathSciNet)
MR1920692

Zentralblatt MATH identifier
1031.35094

Subjects
Primary: 93D15: Stabilization of systems by feedback
Secondary: 35B45: A priori estimates 35L05: Wave equation 35Q72 93C20: Systems governed by partial differential equations

Citation

Astaburuaga, María Angélica; Coimbra Charão, Ruy. Stabilization of the total energy for a system of elasticity with localized dissipation. Differential Integral Equations 15 (2002), no. 11, 1357--1376. https://projecteuclid.org/euclid.die/1356060727


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