Global existence and uniform decay rates for the Kirchhoff-Carrier equation with nonlinear dissipation

Abstract

This paper is devoted to the existence of global solutions of the \newline Kirchhoff-Carrier equation $$u_{tt}-M\bigl(t,\int_{\Omega}\left|\nabla u\right|^2dx\bigr)\Delta u=0$$ subject to nonlinear boundary dissipation. Assuming that $M(t,\lambda )\geq m_0>0$, we prove the existence and uniqueness of regular solutions without any smallness on the initial data. Moreover, uniform decay rates are obtained by assuming a nonlinear feedback acting on the boundary.