On the Asymptotic Behaviour of a Singular Hyperbolic Equation with Nonlocal Boundary Conditions

Abstract

In this paper, we consider one-dimentional of degenerate and singular wave equations with the fractional feedback acting on one end only. First, we reformulate each system into an augmented model and using a general criteria of Arendt-Batty, we prove that our models are strongly stable. Next, by using a spectrum method, we establish nonuniform stabilization. Using a frequency domain approach we prove some polynomial energy decay rate depending on the order of the fractional derivative.