Asymptotic stability of wave equations coupled by velocities

TL;DR

This paper investigates the conditions under which coupled wave equations with constant coefficients exhibit exponential stability, providing a comprehensive analysis using multiple mathematical approaches and determining the optimal decay rate in one dimension.

Contribution

It introduces a necessary and sufficient condition for exponential stability of coupled wave equations and derives the optimal decay rate in one-dimensional cases.

Findings

Exponential stability is achieved under specific coefficient conditions.

The optimal decay rate is established for one-dimensional systems.

Multiple analytical methods confirm the stability criteria.

Abstract

This paper is devoted to study the asymptotic stability of wave equations with constant coefficients coupled by velocities. By using Riesz basis approach, multiplier method and frequency domain approach respectively, we find the sufficient and necessary condition, that the coefficients satisfy, leading to the exponential stability of the system. In addition, we give the optimal decay rate in one dimensional case.