Existence and uniqueness results for a nonlinear stationary system

TL;DR

This paper establishes existence and partial uniqueness results for a nonlinear stationary thermoviscoelastic system with $L^1$ coupling terms, employing renormalized solution techniques for elliptic equations.

Contribution

It introduces novel existence and partial uniqueness results for a coupled thermoviscoelastic system involving $L^1$ data, using renormalized solution methods.

Findings

Existence of solutions for the nonlinear stationary system.

Partial uniqueness results for the coupled system.

Application of renormalized solution techniques to $L^1$ coupling terms.

Abstract

We prove a few existence results of a solution for a static system with a coupling of thermoviscoelastic type. As this system involves $L^1$ coupling terms we use the techniques of renormalized solutions for elliptic equations with $L^1$ data. We also prove partial uniqueness results.