A general decay and optimal decay result in a heat system with a viscoelastic term

TL;DR

This paper establishes a general and optimal decay result for a quasilinear heat system with a viscoelastic term, improving and broadening previous stability findings.

Contribution

It introduces a unified decay framework for heat systems with viscoelastic effects, enhancing the understanding of their stability behavior.

Findings

Proves a general decay rate applicable to a class of heat systems with viscoelastic terms.

Improves upon existing stability results by providing more comprehensive decay estimates.

Demonstrates the optimality of the decay results in the context of the studied systems.

Abstract

We consider a quasilinear heat system in the presence of an integral term and establish a general and optimal decay result from which improves and generalizes several stability results in the literature.