Exponential decay  innon-uniform porous-thermo-elasticity model of Lord-Shulman type

Zhong-Jie Han; Gen-Qi Xu

doi:10.3934/dcdsb.2012.17.57

Article Contents

2012, Volume 17, Issue 1: 57-77. Doi: 10.3934/dcdsb.2012.17.57

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Exponential decay in non-uniform porous-thermo-elasticity model of Lord-Shulman type

Zhong-Jie Han^1, and
Gen-Qi Xu^1,

1.
Department of Mathematics, Tianjin University, Tianjin 300072

Received: September 2010

Revised: July 2011

Published: January 2012

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Abstract

The spectrum and asymptotic behavior of the non-uniform porous-thermo-elasticity of Lord-Shulman type is considered in this paper. It is shown that the corresponding system operator generates a $C_0$ semigroup of contractions in an appropriate Hilbert space setting. By a detailed spectral analysis, the asymptotic expressions of the spectrum of the system is gotten. Based on the spectral property, the Riesz basis property of the (generalized) eigenvectors is proved, which implies that the system satisfies the spectrum-determined-growth condition. Then the exponential stability of this system is deduced from the distribution of the spectrum.

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Mathematics Subject Classification: Primary: 35B40, 35P20; Secondary: 74F05.

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