The Stability of a Coupled Degenerate Wave System Under Boundary Control
Ya-nan Sun, Qiong Zhang
TL;DR
This paper proves polynomial stability of a coupled degenerate wave system with boundary control using weighted inequalities and frequency domain methods, highlighting the influence of degeneracy degree.
Contribution
It introduces new stability analysis techniques for coupled degenerate wave systems, emphasizing the role of degeneracy degree in stability behavior.
Findings
The coupled system is polynomially stable.
Stability depends on the degree of degeneracy.
Weighted inequalities and frequency domain methods are effective.
Abstract
In this paper, we investigate a system composed of two degenerate wave equations which are connected at one point. By introducing some inequalities on the weighted spaces and employing the frequency domain method, we prove that the system is polynomially stable,which depends on the degree of the degeneracy.
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