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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2008, Volume 48, Number 11, Pages 2024–2041 (Mi zvmmf87)  
This article is cited in 6 scientific papers (total in 6 papers)

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
Full-text PDF (1755 kB) Citations (6)
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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.
Received: 09.04.2007
Revised: 18.03.2008
English version:
Computational Mathematics and Mathematical Physics, 2008, Volume 48, Issue 11, Pages 2059–2076
DOI: https://doi.org/10.1134/S0965542508110110
Bibliographic databases:
Document Type: Article
UDC: 519.63
Language: Russian
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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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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