Asymptotic behavior of the wave equation under time-dependent fractional damping

Abstract

In this paper, we analyze the stabilization of a wave equation subject to a fractional damping term that varies with time. We begin by proving the well-posedness of the system through the framework of semigroup theory for linear operators. Subsequently, we establish the strong stability of the solution. Furthermore, we derive general estimates for the energy decay rates. The methodology integrates tools from frequency domain analysis and multiplier techniques.