Global weak solution, uniqueness and exponential decay for a class of degenerate hyperbolic equation

This paper deals with existence, uniqueness and energy decay of solutions to a degenerate hyperbolic equations given by \begin{align*} K(x,t)u'' - M\left(\int_\Omega |\nabla u|^2\,dx \right) \Delta u u' = 0, \end{align*} operator coefficient $K(x,t)$ satisfying suitable properties $M(\,\cdot \,) \in C^1([0, \infty))$ is function which greatest lower bound for $ M (\,\cdot\,) zero. For global weak solution we use the Faedo-Galerkin method. Exponential proven using theorem due M. Nakao.