Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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On a contact problem in thermoelasticity with second sound


Author: Jan Sprenger
Journal: Quart. Appl. Math. 67 (2009), 601-615
MSC (2000): Primary 35Q99
DOI: https://doi.org/10.1090/S0033-569X-09-01132-7
Published electronically: July 29, 2009
MathSciNet review: 2588226
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Abstract: We investigate the existence and stability of a thermoelastic contact problem with second sound. Previous results established the existence and stability of a solution of the corresponding classical system in the case of radial symmetry. However, recent works have shown that sometimes stability can be lost when the classical Fourier heat conduction is substituted by Cattaneo's Law. We show that also in this case this substitution does indeed lead to a loss in regularity that proves to be a major problem prohibiting the transfer of the existence proof for the classical problem to the problem with second sound, leaving the existence of a solution an open question. We then prove that, if a viscoelastic term is added to the equations, providing additional regularity, then existence and exponential stability (the second, as can be expected, only in the case of radial symmetry) will follow.


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Additional Information

Jan Sprenger
Affiliation: Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstrasse 8-10, 1040 Wien, Austria
Email: jsprenger@asc.tuwien.ac.at

DOI: https://doi.org/10.1090/S0033-569X-09-01132-7
Received by editor(s): March 18, 2008
Published electronically: July 29, 2009
Additional Notes: The author would like to thank Professor Dr. Racke for helpful suggestions and the opportunity to work on this topic.
Article copyright: © Copyright 2009 Brown University
The copyright for this article reverts to public domain 28 years after publication.


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