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Averaging Method for Quasi-Linear Hyperbolic Systems

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Abstract

The paper considers the Cauchy problem for a multidimensional quasilinear hyperbolic system of differential equations with the data rapidly oscillating in time. This data do not explicitly depend on spatial variables. The method by N. M. Krylov–N. N. Bogolyubov is developed and justified for these systems. Also an algorithm is developed and justified, based on this method and the method of two-scale expansions, for constructing the complete asymptotics of solutions.

DOI 10.1134/S1061920823040118

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Funding

The research was carried out with the support of the Russian Science Foundation (project no. 20-11-20141, https://rscf.ru/project/23-11-45003/).

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Authors and Affiliations

  1. Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia

    V.B. Levenshtam

  2. Southern Federal University, Rostov-on-Don, Russia

    V.B. Levenshtam

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  1. V.B. Levenshtam
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Correspondence to V.B. Levenshtam.

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Levenshtam, V. Averaging Method for Quasi-Linear Hyperbolic Systems. Russ. J. Math. Phys. 30, 552–560 (2023). https://doi.org/10.1134/S1061920823040118

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  • DOI: https://doi.org/10.1134/S1061920823040118

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