RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Trudy MIAN:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Tr. Mat. Inst. Steklova, 2013, Volume 281, Pages 170–187 (Mi tm3469)  

This article is cited in 4 scientific papers (total in 5 papers)

Homogenization and dispersion effects in the problem of propagation of waves generated by a localized source

V. V. Grushinab, S. Yu. Dobrokhotovac, S. A. Sergeevac

a Moscow Institute of Physics and Technology (State University), Dolgoprudnyi, Russia
b Moscow State Institute of Electronics and Mathematics — Higher School of Economics, Moscow, Russia
c Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia

Abstract: We construct asymptotic solutions to the wave equation with velocity rapidly oscillating against a smoothly varying background and with localized initial perturbations. First, using adiabatic approximation in the operator form, we perform homogenization that leads to a linearized Boussinesq-type equation with smooth coefficients and weak “anomalous” dispersion. Then, asymptotic solutions to this and, as a consequence, to the original equations are constructed by means of a modified Maslov canonical operator; for initial perturbations of special form, these solutions are expressed in terms of combinations of products of the Airy functions of a complex argument. On the basis of explicit formulas obtained, we analyze the effect of fast oscillations of the velocity on the solution fronts and solution profiles near the front.

DOI: https://doi.org/10.1134/S0371968513020143

Full text: PDF file (642 kB)
References: PDF file   HTML file

English version:
Proceedings of the Steklov Institute of Mathematics, 2013, 281, 161–178

Bibliographic databases:

UDC: 517.9
Received in September 2012

Citation: V. V. Grushin, S. Yu. Dobrokhotov, S. A. Sergeev, “Homogenization and dispersion effects in the problem of propagation of waves generated by a localized source”, Modern problems of mechanics, Collected papers. Dedicated to Academician Andrei Gennad'evich Kulikovskii on the occasion of his 80th birthday, Tr. Mat. Inst. Steklova, 281, MAIK Nauka/Interperiodica, Moscow, 2013, 170–187; Proc. Steklov Inst. Math., 281 (2013), 161–178

Citation in format AMSBIB
\Bibitem{GruDobSer13}
\by V.~V.~Grushin, S.~Yu.~Dobrokhotov, S.~A.~Sergeev
\paper Homogenization and dispersion effects in the problem of propagation of waves generated by a~localized source
\inbook Modern problems of mechanics
\bookinfo Collected papers. Dedicated to Academician Andrei Gennad'evich Kulikovskii on the occasion of his 80th birthday
\serial Tr. Mat. Inst. Steklova
\yr 2013
\vol 281
\pages 170--187
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3469}
\crossref{https://doi.org/10.1134/S0371968513020143}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3479940}
\elib{http://elibrary.ru/item.asp?id=20193387}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2013
\vol 281
\pages 161--178
\crossref{https://doi.org/10.1134/S0081543813040147}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000322390600014}
\elib{http://elibrary.ru/item.asp?id=23980693}


Linking options:
  • http://mi.mathnet.ru/eng/tm3469
  • https://doi.org/10.1134/S0371968513020143
  • http://mi.mathnet.ru/eng/tm/v281/p170

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
    Erratum

    This publication is cited in the following articles:
    1. V. V. Grushin, S. Yu. Dobrokhotov, “Homogenization in the Problem of Long Water Waves over a Bottom Site with Fast Oscillations”, Math. Notes, 95:3 (2014), 324–337  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    2. V. V. Grushin, S. Yu. Dobrokhotov, S. A. Sergeev, “Correction to the paper “Homogenization and dispersion effects in the problem of propagation of waves generated by a localized source” (Proc. Steklov Inst. Math. 281, 161–178 (2013))”, Proc. Steklov Inst. Math., 288 (2015), 265–265  mathnet  crossref  crossref  isi  elib
    3. Dobrokhotov S.Yu., Nazaikinskii V.E., Tirozzi B., “on a Homogenization Method For Differential Operators With Oscillating Coefficients”, Dokl. Math., 91:2 (2015), 227–231  crossref  mathscinet  zmath  isi  elib  scopus
    4. Dobrokhotov S.Yu., Grushin V.V., Sergeev S.A., Tirozzi B., “Asymptotic theory of linear water waves in a domain with nonuniform bottom with rapidly oscillating sections”, Russ. J. Math. Phys., 23:4 (2016), 455–474  crossref  mathscinet  zmath  isi  elib  scopus
    5. D. A. Karaeva, A. D. Karaev, V. E. Nazaikinskii, “Homogenization method in the problem of long wave propagation from a localized source in a basin over an uneven bottom”, Differ. Equ., 54:8 (2018), 1057–1072  crossref  crossref  isi  elib  elib  scopus
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
    Number of views:
    This page:325
    Full text:27
    References:50

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019