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 Izv. RAN. Ser. Mat., 1992, Volume 56, Issue 4, Pages 813–851 (Mi izv928)

Averaging of quasilinear parabolic equations with rapidly oscillating principal part. Exponential dichotomy

V. B. Levenshtam

Rostov State University

Abstract: The first part of this article is an investigation of the question of preservation of an exponential dichotomy for solutions of a linear parabolic equation upon a high-frequency perturbation of its principal terms. The second part contains a justification of the averaging principle on the whole time axis for quasilinear parabolic equations with rapidly oscillating principal part.

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English version:
Russian Academy of Sciences. Izvestiya Mathematics, 1993, 41:1, 95–132

Bibliographic databases:

UDC: 519.4+513.88
MSC: Primary 35K30, 35K55; Secondary 35B20, 34C29

Citation: V. B. Levenshtam, “Averaging of quasilinear parabolic equations with rapidly oscillating principal part. Exponential dichotomy”, Izv. RAN. Ser. Mat., 56:4 (1992), 813–851; Russian Acad. Sci. Izv. Math., 41:1 (1993), 95–132

Citation in format AMSBIB
\Bibitem{Lev92} \by V.~B.~Levenshtam \paper Averaging of quasilinear parabolic equations with rapidly oscillating principal part. Exponential dichotomy \jour Izv. RAN. Ser. Mat. \yr 1992 \vol 56 \issue 4 \pages 813--851 \mathnet{http://mi.mathnet.ru/izv928} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1208152} \zmath{https://zbmath.org/?q=an:0795.35041} \adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1993IzMat..41...95L} \transl \jour Russian Acad. Sci. Izv. Math. \yr 1993 \vol 41 \issue 1 \pages 95--132 \crossref{https://doi.org/10.1070/IM1993v041n01ABEH002253} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1993LZ84700005} 

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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. Levenshtam V., “Senior Approximation of Averaging Method for Quasi-Linear Parabolic Equations”, Dokl. Akad. Nauk, 353:5 (1997), 599–601
2. V. B. Levenshtam, “Higher approximations of the averaging method for quasilinear parabolic equations with a rapidly oscillating principal part in the case of the Cauchy problem”, Math. Notes, 65:4 (1999), 470–478
3. V. B. Levenshtam, “On an averaging method for quasilinear parabolic equations with rapidly oscillating coefficients”, Russian Math. (Iz. VUZ), 44:7 (2000), 20–28
4. V. B. Levenshtam, “Unique Solvability of Parabolic Equations with Almost-Periodic Coefficients in Hölder Spaces”, Math. Notes, 73:6 (2003), 813–828
5. V. B. Levenshtam, “Uniform exponential dichotomy of parabolic operators with rapidly oscillating coefficients”, Math. Notes, 79:5 (2006), 675–680
6. A. Atencio, “Separation of Chiral Molecules: A Way to Homochirality”, Orig Life Evol Biosph, 2012
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