Geodesic
Curvilinear parallelogram identity and mean-value property for a semilinear hyperbolic equation of the second order
Eurasian mathematical journal, Tome 15 (2024) no. 2, pp. 61-74

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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 problems. 
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     title = {Curvilinear parallelogram identity and mean-value property for a semilinear hyperbolic equation of the second order},
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V. I. Korzyuk; J. V. Rudzko. Curvilinear parallelogram identity and mean-value property for a semilinear hyperbolic equation of the second order. Eurasian mathematical journal, Tome 15 (2024) no. 2, pp. 61-74. http://geodesic.mathdoc.fr/item/EMJ_2024_15_2_a4/