GLOBAL EXISTENCE AND ENERGY DECAY ESTIMATE OF SOLUTIONS FOR A CLASS OF NONLINEAR HIGHER-ORDER WAVE EQUATION WITH GENERAL NONLINEAR DISSIPATION AND SOURCE TERM

摘要

This paper deals with a higher-order wave equation with general nonlinear dissipation and source term u" + (-∆)~mu + 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.