Global existence and blowup of solutions for a class of nonlinear wave equations with linear pseudo-differential operator

Abstract

This paper pays attention to the Cauchy problem for a class of nonlinear wave equations with linear pseudo-differential operator. In the framework of variational arguments, the existence and nonexistence of global solution to this problem are derived when the total initial energy is less than or equal to the mountain pass level. Further, a finite-time blowup result for arbitrarily high initial energy is established.