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

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Abstract

Systems of first-order semilinear partial differential equations with terms that oscillate at a frequency ω ≫ 1 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.

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Authors and Affiliations

  1. Southern Scientific Center, ul. Milchakova 8a, Rostov-on-Don, 344090, Russia

    A. K. Kapikyan & V. B. Levenshtam

Authors
  1. A. K. Kapikyan
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  2. V. B. Levenshtam
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Correspondence to V. B. Levenshtam.

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Original Russian Text © A.K. Kapikyan, V.B. Levenshtam, 2008, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2008, Vol. 48, No. 11, pp. 2024–2041.

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Kapikyan, A.K., Levenshtam, V.B. First-order partial differential equations with large high-frequency terms. Comput. Math. and Math. Phys. 48, 2059–2076 (2008). https://doi.org/10.1134/S0965542508110110

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  • DOI: https://doi.org/10.1134/S0965542508110110

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