Indirect boundary stabilization for weakly coupled degenerate wave equations under fractional damping

Abstract

In this paper, we consider the well-posedness and stability of a one-dimensional system of degenerate wave equations coupled via zero order terms with one boundary fractional damping acting on one end only. We prove optimal polynomial energy decay rate of order $1/t^{(3-\tau )}$. The method is based on the frequency domain approach combined with multiplier technique.