Interior feedback stabilization of wave equations with dynamic boundary delay

TL;DR

This paper investigates the stabilization of wave equations with dynamic boundary delay using interior feedback, establishing stability results through frequency domain methods and multiplier techniques.

Contribution

It introduces a novel approach to stabilize wave equations with boundary delays by applying a specific damping operator and advanced analytical techniques.

Findings

Stability is achieved under certain damping conditions.

Frequency domain analysis confirms the effectiveness of the feedback.

The method extends existing stabilization techniques to delayed boundary scenarios.

Abstract

In this paper we consider an interior stabilization problem for the wave equation with dynamic boundary delay.We prove some stability results under the choice of damping operator. The proof of the main result is based on a frequency domain method and combines a contradiction argument with the multiplier technique to carry out a special analysis for the resolvent.