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.

中文翻译：

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一类带有线性伪微分算子的非线性波动方程解的整体存在和爆破

本文关注一类带有线性伪微分算子的非线性波动方程的柯西问题。在变分论证的框架中，当总初始能量小于或等于山口水平时，就可以得出该问题整体解决方案的存在和不存在。此外，建立了任意高初始能量的有限时间爆燃结果。