On global existence and asymptotic stability of solutions of mildly degenerate dissipative nonlinear wave equations of Kirchhoff type

Abstract

We consider the global existence and asymptotic stability of solutions to the Cauchy problem for degenerate nonlinear wave equations of Kirchhoff type with a dissipative term in unbounded domain. We derive the sharp decay estimates of the solution and its derivatives. Moreover, we show that the solution has a lower decay estimate of some algebraic rate.