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

Abstract

Existence of a very weak solution to the d d -dimensional thermo-visco-elasticity system for Kelvin-Voigt-type material at small strains involving (possibly nonlinear) monotone viscosity of a p p -Laplacian type and temperature-dependent heat capacity of an ( ω − 1 ) (\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 L^1 -structure is obtained under the conditions p ≥ 2 p\ge 2 , ω ≥ 1 \omega \ge 1 , and p > 1 + d / ( 2 ω ) p>1+d/(2\omega ) .