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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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

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

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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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