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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
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
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
Linking options:
https://www.mathnet.ru/eng/emj502 https://www.mathnet.ru/eng/emj/v15/i2/p61
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Statistics & downloads: |
Abstract page: | 62 | Full-text PDF : | 20 | References: | 11 |
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