Global existence and energy decay of solutions for Kirchhoff-Carrier equations with weakly nonlinear dissipation

Abstract

In this paper we prove the global existence and study decay property of the solutions to the initial boundary value problem for the solutions to the quasilinear wave equation of Kirchhoff-Carrier type with a general weakly nonlinear dissipative term by constructing a stable set in $H^{2}\bigcap H_{0}^{1}$. }