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August  2003, 3(3): 383-400. doi: 10.3934/dcdsb.2003.3.383

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, Spain
2. 

Department of Mathematics and Statistics, University of Konstanz, 78457 Konstanz

Received  October 2002 Revised  January 2003 Published  May 2003

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.
Keywords: exponential stability, Hyperbolic thermoelasticity, radial symmetry., equipartition of energy.
Mathematics Subject Classification: 74F0.
Citation: Ramon Quintanilla, Reinhard Racke. Stability in thermoelasticity of type III. Discrete and Continuous Dynamical Systems - B, 2003, 3 (3) : 383-400. doi: 10.3934/dcdsb.2003.3.383
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