Exponential decay for semilinear wave equations with viscoelastic damping and delay feedback

TL;DR

This paper investigates the exponential decay of solutions to semilinear wave equations with viscoelastic damping and delay feedback, establishing well-posedness and decay estimates for small initial data.

Contribution

It extends previous analysis by proving exponential decay for a broader class of semilinear wave equations with variable coefficient damping and delay.

Findings

Proved well-posedness of the equations under certain conditions.

Established exponential decay estimates for small initial data.

Extended previous results to include variable coefficients and delay feedback.

Abstract

In this paper we study a class of semilinear wave type equations with viscoelastic damping and delay feedback with time variable coefficient. By combining semigroup arguments, careful energy estimates and an iterative approach we are able to prove, under suitable assumptions, a well-posedness result and an exponential decay estimate for solutions corresponding to small initial data. This extends and concludes the analysis initiated in [16] and then developed in [13, 17].