# General enegy decay for a viscoelastic equation of Kirchhoff type with acoustic boundary conditions

## TL;DR

This paper investigates the global existence and energy decay of solutions to a viscoelastic Kirchhoff-type equation with acoustic boundary conditions, extending decay results to a broader class of relaxation functions.

## Contribution

It establishes global existence and general energy decay for a viscoelastic Kirchhoff equation with acoustic boundary conditions, using a novel approach to relaxation functions.

## Key findings

- Solutions exist globally under certain initial conditions.
- Energy decays over time for a wider class of relaxation functions.
- The decay rate is characterized using a lemma of P. Martinez.

## Abstract

This paper is concerned with a viscoelastic equation of Kirchhoff type with acoustic boundary conditions in a bounded domain of $\mathbb{R}^{n}.$ We show that, under suitable conditions on the initial data, the solution exists globally in time. Then, we prove the general energy decay of global solutions by applying a lemma of P. Martinez, wihch allows us to get our decay result for a class of relaxation functions wider than that usually used.