Formation of singularities in one-dimensional thermoelasticity with second sound

Hu, Yuxi; Racke, Reinhard

doi:10.1090/S0033-569X-2014-01336-2

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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