RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find






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


Mat. Zametki, 2018, Volume 104, Issue 4, Pages 483–504 (Mi mz11884)  

This article is cited in 1 scientific paper (total in 1 paper)

Simple Asymptotics for a Generalized Wave Equation with Degenerating Velocity and Their Applications in the Linear Long Wave Run-Up Problem

A. Yu. Anikinab, S. Yu. Dobrokhotovab, V. E. Nazaikinskiiab

a Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow
b Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region

Abstract: Asymptotic solutions of the wave equation degenerating on the boundary of the domain (where the wave propagation velocity vanishes as the square root of the distance from the boundary) can be represented with the use of a modified canonical operator on a Lagrangian submanifold, invariant with respect to the Hamiltonian vector field, of the nonstandard phase space constructed by the authors in earlier papers. The present paper provides simple expressions in a neighborhood of the boundary for functions represented by such a canonical operator and, in particular, for the solution of the Cauchy problem for the degenerate wave equation with initial data localized in a neighborhood of an interior point of the domain.

Keywords: wave equation, nonstandard characteristics, run-up on a sloping beach, localized source, near-boundary asymptotics.

Funding Agency Grant Number
Russian Science Foundation 16-11-10282
This work was supported by the Russian Science Foundation under grant 16-11-10282 in accordance with paragraph 17.7 of Sec. 3.1. and paragraph (7) of Sec. 3.2 of the work schedule for this grant for the year 2017.


DOI: https://doi.org/10.4213/mzm11884

Full text: PDF file (664 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Mathematical Notes, 2018, 104:4, 471–488

Bibliographic databases:

Document Type: Article
UDC: 517.9
Received: 11.12.2017

Citation: A. Yu. Anikin, S. Yu. Dobrokhotov, V. E. Nazaikinskii, “Simple Asymptotics for a Generalized Wave Equation with Degenerating Velocity and Their Applications in the Linear Long Wave Run-Up Problem”, Mat. Zametki, 104:4 (2018), 483–504; Math. Notes, 104:4 (2018), 471–488

Citation in format AMSBIB
\Bibitem{AniDobNaz18}
\by A.~Yu.~Anikin, S.~Yu.~Dobrokhotov, V.~E.~Nazaikinskii
\paper Simple Asymptotics for a Generalized Wave Equation with Degenerating Velocity and Their Applications in the Linear Long Wave Run-Up Problem
\jour Mat. Zametki
\yr 2018
\vol 104
\issue 4
\pages 483--504
\mathnet{http://mi.mathnet.ru/mz11884}
\crossref{https://doi.org/10.4213/mzm11884}
\elib{http://elibrary.ru/item.asp?id=35601233}
\transl
\jour Math. Notes
\yr 2018
\vol 104
\issue 4
\pages 471--488
\crossref{https://doi.org/10.1134/S0001434618090158}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000451315200015}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85056738402}


Linking options:
  • http://mi.mathnet.ru/eng/mz11884
  • https://doi.org/10.4213/mzm11884
  • http://mi.mathnet.ru/eng/mz/v104/i4/p483

    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

    This publication is cited in the following articles:
    1. Anatoly Anikin, Sergey Dobrokhotov, Vladimir Nazaikinskii, “Asymptotic solutions of the wave equation with degenerate velocity and with right-hand side localized in space and time”, Zhurn. matem. fiz., anal., geom., 14:4 (2018), 393–405  mathnet  crossref
  • Математические заметки Mathematical Notes
    Number of views:
    This page:134
    References:12
    First page:22

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