Global existence and asymptotic behavior for a mildly degenerate kirchhoff wave equation with boundary damping

In this article a degenerate nonlinear dissipative wave equation of Kirchhoff type with nonlinear boundary damping is considered. We prove the existence, uniqueness and regularity of the global solution of the system when the initial data are small enough and the geometry of the domain satisfies suitable assumptions. We also obtain the polynomial decay property of the global solution.