Existence of weak solutions of an unsteady thermistor problem with p-Laplacian type equation

TL;DR

This paper proves the existence of weak solutions for an unsteady thermistor system modeled by a p-Laplacian type equation, where the electrical conductivity depends monotonically on the electric field, advancing mathematical understanding of thermistor behavior.

Contribution

It establishes the existence of weak solutions for a thermistor model with p-Laplacian type equations, considering monotone electrical conductivity functions.

Findings

Existence of weak solutions proven for the thermistor system.

Mathematical framework developed for p-Laplacian type equations.

Results applicable to thermistor materials with monotone conductivity functions.

Abstract

We prove the existence of weak solutions to an unsteady thermistor system with p-Laplacian type equation for the electrostatic potential, where the electrical conductivity of the thermistor material is a monotone function of the electric field density.