Feedback boundary stabilization of wave equations with interior delay

TL;DR

This paper addresses the boundary stabilization of wave equations with interior delay, proving exponential stability under geometric conditions using Lyapunov functionals and multiplier identities.

Contribution

It introduces a novel stabilization method for wave equations with interior delay, establishing exponential decay under specific geometric conditions.

Findings

Exponential stability of the wave equation with interior delay

Development of a Lyapunov functional for stability analysis

Use of multiplier identities to prove decay estimates

Abstract

In this paper we consider a boundary stabilization problem for the wave equation with interior delay. We prove an exponential stability result under some Lions geometric condition. The proof of the main result is based on an identity with multipliers that allows to obtain a uniform decay estimate for a suitable Lyapunov functional.