Stability in thermoelasticity of type III

Ramon Quintanilla; Reinhard Racke

doi:10.3934/dcdsb.2003.3.383

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2003, Volume 3, Issue 3: 383-400. Doi: 10.3934/dcdsb.2003.3.383

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Stability in thermoelasticity of type III

Ramon Quintanilla^1, and
Reinhard Racke^2,

1.
Department of Applied Mathematics II, UPC Terrassa, Colom 11, 08222 Terrassa
2.
Department of Mathematics and Statistics, University of Konstanz, 78457 Konstanz

Received: September 30, 2002

Revised: December 31, 2002

Published: July 2003

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Abstract

We consider initial-boundary value problems in a hyperbolic thermoelastic system, called thermoelasticity of type III. First, we prove the exponential stability in one space dimension for different boundary conditions with energy methods and spectral methods, respectively. Then the exponential stability in more two or three space dimensions is proved for radially symmetric situations. Finally, the equipartition of energy is investigated.

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Mathematics Subject Classification: 74F05.

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