Thermo-visco-elasticity at Small Strains with L-data

Existence of a very weak solution to the d-dimensional thermo-viscoelasticity 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 (ω−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-structure is obtained under the conditions p ≥ 2, ω ≥ 1, and p > 1 + d/(2ω).