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2006 On the stabilization of dynamic elasticity equations with unbounded locally distributed dissipation
L. R. Tcheugoue Tebou
Differential Integral Equations 19(7): 785-798 (2006).

Abstract

We consider the dynamic elasticity equations with a locally distributed damping in a bounded domain. The local dissipation of the form $a(x)y_{t}$ allows coefficients $a$ that lie in some $L^r(\Omega)$, with $(r>2)$. Using multiplier techniques, interpolation inequalities, and a judicious application of the Hölder inequality, we prove sharp energy decay estimates for all $r>Max(2,N)$, where $N$ denotes the space dimension. All space dimensions are considered; the results obtained generalize and improve earlier works where $r$ is required to satisfy $r \! \geq \! {3N+\sqrt{9N^2-16N}\over4}$, for $N\geq3$.

Citation

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L. R. Tcheugoue Tebou. "On the stabilization of dynamic elasticity equations with unbounded locally distributed dissipation." Differential Integral Equations 19 (7) 785 - 798, 2006.

Information

Published: 2006
First available in Project Euclid: 21 December 2012

zbMATH: 1212.93260
MathSciNet: MR2235895

Subjects:
Primary: 93D15
Secondary: 35Q72 , 74H55 , 74M05

Rights: Copyright © 2006 Khayyam Publishing, Inc.

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Vol.19 • No. 7 • 2006
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