Large data solutions for semilinear higher order equations

Abstract

In this paper we study local and global in time existence for a class of nonlinear evolution equations having order eventually greater than 2 and not integer. The linear operator has an homogeneous damping term; the nonlinearity is of polynomial type without derivatives: \begin{document}$ u_{tt}+ (-\Delta)^{2\theta}u+2\mu(-\Delta)^\theta u_t + |u|^{p-1}u = 0, \quad t\geq0, x\in {\mathbb{R}}^n, $\end{document} with \begin{document}$ \mu>0 $\end{document} , \begin{document}$ \theta>0 $\end{document} . Since we are treating an absorbing nonlinear term, large data solutions can be considered.