CURVILINEAR PARALLELOGRAM IDENTITY AND MEAN-VALUE PROPERTY FOR A SEMILINEAR HYPERBOLIC EQUATION OF THE SECOND ORDER

Abstract

In this paper, we discuss some of important qualitative properties of solutions of second-order hyperbolic equations, whose coefficients of the terms involving the second-order derivatives are independent of the desired function and its derivatives. Solutions of these equations have a special property called curvilinear parallelogram identity (or mean-value property), which can be used to solve some initial-boundary value problem