Thermo-visco-elasticity at small strains with 𝐿¹-data

Roubíček, Tomáš

doi:10.1090/S0033-569X-09-01094-3

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

Author: Tomáš Roubíček
Journal: Quart. Appl. Math. 67 (2009), 47-71
MSC (2000): Primary 74F05; Secondary 35K55, 74H20, 80A17
DOI: https://doi.org/10.1090/S0033-569X-09-01094-3
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 $p\ge 2$, $\omega \ge 1$, and $p>1+d/(2\omega )$.

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