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 \begin{document}$u''+(-Δ)^mu+g(u')=b|u|^{p-2}u, $ \end{document} 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.