Exponential Stability for Degenerate/Singular Hyperbolic Equations with Delayed Boundary Feedback

Abstract

In this paper, we consider a degenerate/singular wave equation that is fixed at the point where the degeneracy occurs and stabilized with a time-delayed boundary feedback at the other endpoint. First, we study the well-posedness of the system under consideration in appropriate weighted spaces by using semigroup theory. Then, we prove its exponential stability under a suitable condition on both coefficients of the delayed damping term and the not delayed one. Furthermore, an explicit expression of the exponential decay in terms of the system parameters is provided, leveraging both the multiplier method and the Lyapunov functional approach.