A frequency approach for stabilization of one-dimensional degenerate wave equation

Abstract

In this paper, we are concerned with the study of stabilization problem for the following strongly degenerate wave equation in one space dimension $$w_{tt}(x,t)-{\left(x^{\alpha }{w}_x(x,t)\right)}_x=0$$ where $\alpha \in [1,2)$. Thus, using a frequency domain method inspired from \cite{BT}, we prove the polynomial decays of its total energy with $t^{-\nicefrac{1}{2}}$ decay rate.

16 pages, 4 figures