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Zh. Vychisl. Mat. Mat. Fiz., 2008, Volume 48, Number 11, Pages 2024–2041 (Mi zvmmf87)  

First-order partial differential equations with large high-frequency terms

A. K. Kapikyanab, V. B. Levenshtamab

a Southern Scientific Center, ul. Milchakova 8a, Rostov-on-Don, 344090, Russia
b Southern Research Center of the Russian Academy of Sciences

Abstract: Systems of first-order semilinear partial differential equations with terms that oscillate at a frequency $\omega\gg1$ in a single variable and are proportional to $\sqrt\omega$ are considered. The Krylov–Bogolyubov–Mitropol'skii averaging method is substantiated for such equations. Based on the two-scale expansion method, an algorithm for constructing complete asymptotics of solutions is proposed and justified.

Key words: averaging method, symptotic behavior of solutions, first-order partial differential equations.

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English version:
Computational Mathematics and Mathematical Physics, 2008, 48:11, 2059–2076

Bibliographic databases:

UDC: 519.63
Received: 09.04.2007
Revised: 18.03.2008

Citation: A. K. Kapikyan, V. B. Levenshtam, “First-order partial differential equations with large high-frequency terms”, Zh. Vychisl. Mat. Mat. Fiz., 48:11 (2008), 2024–2041; Comput. Math. Math. Phys., 48:11 (2008), 2059–2076

Citation in format AMSBIB
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  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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