Existence result of the global attractor for a triply nonlinear thermistor problem

TL;DR

This paper proves the existence of a universal attractor for a triply nonlinear thermistor problem, demonstrating long-term stability and boundedness of solutions in Sobolev spaces.

Contribution

It establishes the existence and uniqueness of solutions, as well as the presence of an absorbing set and a universal attractor for the nonlinear thermistor model.

Findings

Existence of a bounded weak solution

Existence of an absorbing set and universal attractor

Long-term stability of solutions

Abstract

We study the existence and uniqueness of a bounded weak solution for a triply nonlinear thermistor problem in Sobolev spaces. Furthermore, we prove the existence of an absorbing set and, consequently, the universal attractor.