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Eurasian Mathematical Journal, 2024, Volume 15, Number 2, Pages 61–74
DOI: https://doi.org/10.32523/2077-9879-2024-15-2-61-74
(Mi emj502)
 

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

V. I. Korzyuk, J. V. Rudzko

Department of Mathematical Cybernetics, Belarusian State University, 4 Nezavisimosti Avenue, Minsk, Belarus
References:
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 problems.
Keywords and phrases: hyperbolic equation, characteristics parallelogram, mean-value theorem, mean-value property.
Received: 22.04.2022
Document Type: Article
Language: English
Citation: V. I. Korzyuk, J. V. Rudzko, “Curvilinear parallelogram identity and mean-value property for a semilinear hyperbolic equation of the second order”, Eurasian Math. J., 15:2 (2024), 61–74
Citation in format AMSBIB
\Bibitem{KorRud24}
\by V.~I.~Korzyuk, J.~V.~Rudzko
\paper Curvilinear parallelogram identity and mean-value property for a semilinear hyperbolic equation of the second order
\jour Eurasian Math. J.
\yr 2024
\vol 15
\issue 2
\pages 61--74
\mathnet{http://mi.mathnet.ru/emj502}
\crossref{https://doi.org/10.32523/2077-9879-2024-15-2-61-74}
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