The $L_p$ Unique Solvability of the First Initial Boundary-value Problem for Hyperbolic Systems

Abstract

The main purpose of the paper is to prove the existence, uniqueness and smoothness with respect to time variable of the generalized $L_p$-solution of the first initial boundary value problem for higher hyperbolic systems in cylinders with non-smooth base. We also show that the smoothness with respect to time variable of the generalized $L_p$-solution is independent of the smoothness of base of cylinders.