Curvilinear Parallelogram Identity and Mean-Value Property for a Semilinear Hyperbolic Equation of the Second Order

Abstract

In this paper, we discuss some 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 problems.