Boundary stabilization of a one-dimensional wave equation by a switching time-delay: a theoretical and numerical study

TL;DR

This paper investigates the boundary stabilization of a 1D wave equation with a switching time-delay, establishing well-posedness and analyzing exponential stability through theoretical and numerical methods.

Contribution

It introduces a novel analysis of wave equation stabilization with switching delays, combining theoretical proofs with numerical validation.

Findings

The system is well-posed in the semigroup sense.

Exponential stability depends on an appropriate delay coefficient.

Numerical results support the theoretical stability analysis.

Abstract

This paper deals with the boundary stabilization problem of a one-dimensional wave equation with a switching time-delay in the boundary. We show that the problem is well-posed in the sense of semigroups theory of linear operators. Then, we provide a theoretical and numerical study of the exponential stability of the system under an appropriate delay coefficient.