Global existence and decay estimates for the viscoelastic kirchhoff equation with a delay term

TL;DR

This paper establishes the global existence and decay properties of solutions to a viscoelastic Kirchhoff equation with a delay term, using approximation methods and energy techniques.

Contribution

It introduces a novel analysis of a delayed viscoelastic Kirchhoff equation, proving well-posedness and decay estimates for the first time.

Findings

Global solutions exist and are unique.

Solutions exhibit uniform decay over time.

The method applies to equations with delay terms.

Abstract

In this paper, we consider a viscoelastic kirchhoff equation with a delay term in the internal feedback. By using the Faedo-Galarkin approximation method we prove the well-posedness of the global solutions. Introducing suitable energy, we prove the general uniform decay results.