# Dynamic thermoviscoelastic thermistor problem with contact and nonmonotone friction

## TL;DR

This paper models a complex thermoviscoelastic thermistor system with contact and nonmonotone friction, analyzing its evolution and proving the existence of weak solutions using advanced mathematical techniques.

## Contribution

It introduces a coupled dynamic-thermal-electrical model with nonmonotone friction and establishes existence results for weak solutions.

## Key findings

- Existence of weak solutions for the coupled system.
- Effective use of time delays and a priori estimates.
- Handling of nonmonotone friction in thermoviscoelastic context.

## Abstract

The paper studies the evolution of the thermomechanical and electric state of a thermoviscoelastic thermistor that is in frictional contact with a reactive foundation. The mechanical process is dynamic, while the electric process is quasistatic. Friction is modeled with a nonmonotone relation between the tangential traction and tangential velocity. Frictional heat generation is taken into account and so is the strong dependence of the electric conductivity on the temperature. The mathematical model for the process is in the form of a system that consists of dynamic hyperbolic subdifferential inclusion for the mechanical state coupled with a nonlinear parabolic equation for the temperature and an elliptic equation for the electric potential. The paper establishes the existence of a weak solution to the problem by using time delays, a priori estimates and a convergence method.