Author(s)

Xiaodong Zhu

Abstract

We study decay properties of global solutions for some non-linear damped wave equations, which include three cases: non-degenerate, degenerate, and inhomogeneous damping. A canonical model for such equations is a gener- alized Kirchhoff string. We establish decay properties of solutions in energy norm, and give critical damping conditions for a class of non-linear damping functions. In particular we introduce a Lypunov function which can be used to study the case where damping term strongly depends on time. 1 Introduction We consider the initial-boundary value problem for the following non-linear wave equation (utt - M(|| Vu||2) Aw 4- Q(t, ut) + f(u) = 0 in 7 x 0, where / = [0, oo), 31 is a bounded domain in IR" with smooth boundary dtt. Utt — M(\Vu\%)&u is a generalized wave operator

Keywords