Exponential energy decay of solutions for a system of viscoelastic wave equations of Kirchhoff type with strong damping

TL;DR

This paper proves that solutions to a system of viscoelastic wave equations of Kirchhoff type with strong damping exhibit exponential energy decay under specific conditions on relaxation functions and initial data.

Contribution

It establishes the exponential decay rate of solutions' energy for a viscoelastic wave system of Kirchhoff type with strong damping, under new assumptions.

Findings

Solutions' energy decays exponentially over time.

Decay rate depends on relaxation functions and initial data.

Provides conditions ensuring exponential decay.

Abstract

The initial boundary value problem for a system of viscoelastic wave equations of Kirchhoff type with strong damping is considered. We prove that, under suitable assumptions on relaxation functions and certain initial data, the decay rate of the solutions energy is exponential.