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Mat. Zametki, 2014, Volume 96, Issue 4, Pages 522–538 (Mi mz10142)  

This article is cited in 4 scientific papers (total in 4 papers)

Asymptotic Integration of Linear Parabolic Problems with High-Frequency Coefficients in the Critical Case

V. B. Levenshtamab

a Southern Federal University, Rostov-on-Don
b South Mathematical Institute of VSC RAS

Abstract: For a linear second-order parabolic equation with high-frequency coefficients, the complete asymptotics of time-periodic solutions is constructed and justified. The limit averaged stationary problem is assumed degenerate.

Keywords: linear second-order parabolic equation, parabolic equation with high-frequency coefficients, asymptotics of time-periodic solutions, Dirichlet problem, boundary layer method, semigroup, spectral projection.

DOI: https://doi.org/10.4213/mzm10142

Full text: PDF file (537 kB)
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English version:
Mathematical Notes, 2014, 96:4, 499–513

Bibliographic databases:

UDC: 519.633
Received: 30.08.2012
Revised: 16.10.2013

Citation: V. B. Levenshtam, “Asymptotic Integration of Linear Parabolic Problems with High-Frequency Coefficients in the Critical Case”, Mat. Zametki, 96:4 (2014), 522–538; Math. Notes, 96:4 (2014), 499–513

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. V. Gusachenko, V. B. Levenshtam, “Asymptotic analysis of linear parabolic problems with singularities”, Comput. Math. Math. Phys., 55:1 (2015), 71–84  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    2. Levenshtam V.B., Ishmeev M.R., “Asymptotic Integration of Linear System With High-Frequency Coefficients and Stokes Operator in the Main Part”, Asymptotic Anal., 92:3-4 (2015), 363–376  crossref  mathscinet  zmath  isi  elib  scopus
    3. L. I. Sazonov, “High-frequency asymptotics of solutions of ODE in a Banach space”, Izv. Math., 81:6 (2017), 1234–1252  mathnet  crossref  crossref  adsnasa  isi  elib
    4. 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  crossref  mathscinet  zmath  isi  scopus
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