Renormalised solutions in thermo-visco-plasticity for a Norton-Hoff type model. Part I: the truncated case

TL;DR

This paper proves the existence of global strong solutions for a truncated thermo-visco-plasticity model with Norton-Hoff type inelastic behavior, laying groundwork for solutions without truncation.

Contribution

It introduces a novel proof method using Yosida approximation to establish solutions for a complex thermo-visco-plasticity model with truncation.

Findings

Existence of global strong solutions for the truncated model.

Method based on Yosida approximation and limit passage.

Foundation for analyzing the untruncated model.

Abstract

We prove existence of global in time strong solutions to the truncated thermo- visco-plasticity with an inelastic constitutive function of Norton-Hoff type. This result is a starting point to obtain renoramlised solutions for the considered model without truncations. The method of our proof is based on Yosida approximation of the maximal monotone term and a passage to the limit.