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  Quarterly of Applied Mathematics
Quarterly of Applied Mathematics
  
Online ISSN 1552-4485; Print ISSN 0033-569X
 

Thermo-visco-elasticity at small strains with $ L^1$-data


Author: Tomás Roubícek
Journal: Quart. Appl. Math. 67 (2009), 47-71
MSC (2000): Primary 74F05; Secondary 35K55, 74H20, 80A17
Published electronically: January 8, 2009
MathSciNet review: 2495071
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Abstract: Existence of a very weak solution to the $ d$-dimensional thermo-visco-elasticity system for Kelvin-Voigt-type material at small strains involving (possibly nonlinear) monotone viscosity of a $ p$-Laplacian type and temperature-dependent heat capacity of an $ (\omega{-}1)$-polynomial growth is proved by a successive passage to a limit in a suitably regularized Galerkin approximation and sophisticated a priori estimates for the temperature gradient performed for the coupled system. A global solution for arbitrarily large data having an $ L^1$-structure is obtained under the conditions $ p\ge2$, $ \omega\ge1$, and $ p>1+d/(2\omega)$.


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Additional Information

Tomás Roubícek
Affiliation: Mathematical Institute, Charles University, Sokolovská 83, CZ-186 75 Praha 8, Czech Republic; Institute of Thermomechanics of the ASCR, Dolejškova 5, CZ-182 00 Praha 8, Czech Republic
Email: tomas.roubicek@mff.cuni.cz

DOI: http://dx.doi.org/10.1090/S0033-569X-09-01094-3
PII: S 0033-569X(09)01094-3
Keywords: Thermoviscoelasticity, Kelvin-Voigt materials, very weak solutions.
Received by editor(s): June 4, 2007
Published electronically: January 8, 2009
Additional Notes: This work was created as a research activity of “Nečas center for mathematical modeling” LC 06052 (MŠMT ČR) partly supported also by the grants IAA 107 5402 (GA AV ČR) and MSM 21620839 and 1M06031 (MŠMT ČR) and the research plan AVOZ20760514 (ČR). The author acknowledges comments of Dr. Giusseppe Tomassetti that improved the previous version at a lot of places.
Article copyright: © Copyright 2009 Brown University
The copyright for this article reverts to public domain 28 years after publication.



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