Global existence and energy decay estimate of solutions for a class of nonlinear higher-order wave equation with general nonlinear dissipation and source term

Abstract

This paper deals with a higher-order wave equation with general nonlinear dissipation and source term u + (−∆) m u + g(u) = b|u| p−2 u, which was studied extensively when m = 1, 2 and the nonlinear dissipative term g(u) is a polynomial, i.e., g(u) = a|u | q−2 u. We obtain the global existence of solutions and show the energy decay estimate when m ≥ 1 is a positive integer and the nonlinear dissipative term g does not necessarily have a polynomial grow near the origin.