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 Zh. Vychisl. Mat. Mat. Fiz., 2013, Volume 53, Number 7, Pages 1067–1081 (Mi zvmmf9820)

Linear parabolic problem: High-frequency asymptotics in the critical case

V. V. Gusachenko, E. A. Il'icheva, V. B. Levenshtam

Southern Federal University, Rostov-on-Don

Abstract: A second-order linear parabolic problem with high-frequency terms is considered. The elliptic operator of the corresponding limiting (averaged) problem is assumed to be degenerate. A complete formal asymptotic expansion of a time-periodic solution of the perturbed problem is constructed.

Key words: parabolic problem, high-frequency in time coefficients, degenerate limiting problem, complete asymptotic expansion of a time-periodic solution.

DOI: https://doi.org/10.7868/S0044466913070107

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English version:
Computational Mathematics and Mathematical Physics, 2013, 53:7, 882–895

Bibliographic databases:

UDC: 519.633
Revised: 14.01.2013

Citation: V. V. Gusachenko, E. A. Il'icheva, V. B. Levenshtam, “Linear parabolic problem: High-frequency asymptotics in the critical case”, Zh. Vychisl. Mat. Mat. Fiz., 53:7 (2013), 1067–1081; Comput. Math. Math. Phys., 53:7 (2013), 882–895

Citation in format AMSBIB
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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. V. B. Levenshtam, “Asymptotic Integration of Linear Parabolic Problems with High-Frequency Coefficients in the Critical Case”, Math. Notes, 96:4 (2014), 499–513
2. V. V. Gusachenko, V. B. Levenshtam, “Asymptotic analysis of linear parabolic problems with singularities”, Comput. Math. Math. Phys., 55:1 (2015), 71–84
3. V. B. Levenshtam, M. R. Ishmeev, “Asymptotic integration of linear system with high-frequency coefficients and stokes operator in the main part”, Asymptotic Anal., 92:3-4 (2015), 363–376
4. L. I. Sazonov, “On the Existence of Periodic Solutions of Ordinary Differential Equations with High-Frequency Summands in a Banach Space”, Math. Notes, 101:2 (2017), 310–319
5. L. I. Sazonov, “High-frequency asymptotics of solutions of ODE in a Banach space”, Izv. Math., 81:6 (2017), 1234–1252
6. M. R. Ishmeev, V. B. Levenshtam, “A system of partial differential equations with high-frequency coefficients and Stokes operator in the main part. Asymptotic integration in the case of multiple degeneration”, Russ. J. Math. Phys., 25:3 (2018), 284–299
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