Global Regular Solutions to a Kelvin-Voigt Type Thermoviscoelastic System

TL;DR

This paper proves the existence and uniqueness of global regular solutions for a 3-D Kelvin-Voigt thermoviscoelastic system without requiring small initial data, using advanced a priori estimates and anisotropic Sobolev space theory.

Contribution

It provides the first proof of global regular solutions for this system without small data restrictions, employing a novel approach with anisotropic Sobolev spaces.

Findings

Existence and uniqueness of global regular solutions established.

A priori estimates are derived on arbitrary finite time intervals.

The method applies advanced Sobolev space techniques to a complex thermoviscoelastic system.

Abstract

A classical 3-D thermoviscoelastic system of Kelvin-Voigt type is considered. The existence and uniqueness of a global regular solution is proved without small data assumption. The existence proof is based on the successive approximation method. The crucial part constitute a priori estimates on an arbitrary finite time interval, which are derived with the help of the theory of anisotropic Sobolev spaces with a mixed norm.