A thermo-visco-elastic model for nonlinear materials of Norton-Hoff type with L1 data

The objective of this paper is to demonstrate the existence of weak solutions to the thermo-visco-elasticity system for Kelvin-Voigt-type materials. This system involves a monotone viscosity of a p -Laplacian type and an inelastic constitutive relation of Norton-Hoff type. This article extends the previous work of S. Owczarek and K. Wielgos [43] to include a generalized constitutive function of Norton-Hoff type that depends on the stress tensor and temperature. Furthermore, we significantly improve the result obtained in [43] by increasing the regularity of the temperature function, allowing the range of p to extend from p > 5 to p > 5 2 . Using a more general method than in [43] , specifically the Faedo-Galerkin method, we consider non-homogeneous Neumann boundary conditions for the temperature and initial conditions for the temperature with L 1 regularities. This system conserves total energy and is thermodynamically consistent.