The regularity properties and blow-up of the solutions for nonlocal general wave equations

Abstract

In this paper, the Cauchy problem for nonlocal linear and nonlinear wave equations are studied. The equations include the general differential operators. The existence, uniqueness, -regularity properties and blow-up at finite time of solutions of the Cauchy problem is obtained. By choosing differential operators including in equations, the regularity properties of a different type wave equations are studied.