Curvilinear parallelogram identity and mean-value property for a semilinear hyperbolic equation of second-order

Abstract

In this paper, we discuss some of the 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 the curvilinear parallelogram identity (or the mean-value property), which can be used to solve some initial-boundary value problems.

15 pages, 4 figures, planned to publish in Eurasian Mathematical Journal; v2: fixed typos, improved language