Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Formation of singularities in one-dimensional thermoelasticity with second sound


Authors: Yuxi Hu and Reinhard Racke
Journal: Quart. Appl. Math. 72 (2014), 311-321
MSC (2010): Primary 35L60, 35B44
DOI: https://doi.org/10.1090/S0033-569X-2014-01336-2
Published electronically: February 25, 2014
MathSciNet review: 3186239
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Abstract: We investigate the formation of singularities in thermoelasticity with second sound. Transforming into Euler coordinates and combining ideas from Sideris (1985), used for compressible fluids, and Tarabek (1992), used for small data large time existence in second sound models, we are able to show that there are in general no global smooth solutions for large initial data. In contrast to the situation for classical thermoelasticity, we require largeness of the data itself, not of its derivatives.


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Additional Information

Yuxi Hu
Affiliation: Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China
Email: huyuxi@sjtu.edu.cn

Reinhard Racke
Affiliation: Department of Mathematics and Statistics, University of Konstanz, 78457 Konstanz, Germany
Email: reinhard.racke@uni-konstanz.de

DOI: https://doi.org/10.1090/S0033-569X-2014-01336-2
Received by editor(s): July 4, 2012
Published electronically: February 25, 2014
Article copyright: © Copyright 2014 Brown University

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