Differential and Integral Equations

On the stabilization of dynamic elasticity equations with unbounded locally distributed dissipation

L. R. Tcheugoue Tebou

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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 $N\geq3$.

Article information

Source
Differential Integral Equations, Volume 19, Number 7 (2006), 785-798.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356050350

Mathematical Reviews number (MathSciNet)
MR2235895

Zentralblatt MATH identifier
1212.93260

Subjects
Primary: 93D15: Stabilization of systems by feedback
Secondary: 35Q72 74H55: Stability 74M05: Control, switches and devices ("smart materials") [See also 93Cxx]

Citation

Tcheugoue Tebou, L. R. On the stabilization of dynamic elasticity equations with unbounded locally distributed dissipation. Differential Integral Equations 19 (2006), no. 7, 785--798. https://projecteuclid.org/euclid.die/1356050350


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