Global Existence and Asymptotic Behaviour for a Mildly Degenetate Dissipative Hyperbolic Equation of Kirchhoff Type

Abstract

We consider the mildly degenerate Kirchhoff equation with a dissipative term. We prove that if the nonlinear term is locally Lipschitz continuous and the initial data are small enough then the Cauchy problem is globally well-posed for positive times. Moreover, we study the asymptotic behavior of the solutions