RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor
Subscription

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Algebra i Analiz:
Year:
Volume:
Issue:
Page:
Find






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


Algebra i Analiz, 2006, Volume 18, Issue 3, Pages 158–233 (Mi aa75)  

This article is cited in 8 scientific papers (total in 8 papers)

Expository Surveys

Elastodynamics in domains with edges

S. I. Matyukevich, B. A. Plamenevskii

Saint-Petersburg State University

Abstract: Time-dependent boundary value problems with given displacements or stresses on the boundary of a domain are considered. The purpose is to describe the asymptotics of solutions near the edges of the boundary (including formulas for the “stress intensity factors”). The approach is based on various (energy and weighted) estimates of solutions. The weighted estimates in question are mixed in the sense that, in distinct zones, they involve derivatives of different orders. The method is implemented for problems in the cylinder $\mathbb D\times\mathbb R$, where $\mathbb D$ is an $m$-dimensional wedge, $m\ge 2$, and $\mathbb R$ is the time axis. For the cylinder $G\times\mathbb R$, where $G$ is a bounded domain with edges on the boundary, all the steps of the method are described except for the final one, which is related to the asymptotics itself. This step consists in compiling some known results of the theory of elliptic boundary value problems.

Full text: PDF file (581 kB)
References: PDF file   HTML file

English version:
St. Petersburg Mathematical Journal, 2007, 18:3, 459–510

Bibliographic databases:

MSC: 35L30, 35L35
Received: 01.12.2005

Citation: S. I. Matyukevich, B. A. Plamenevskii, “Elastodynamics in domains with edges”, Algebra i Analiz, 18:3 (2006), 158–233; St. Petersburg Math. J., 18:3 (2007), 459–510

Citation in format AMSBIB
\Bibitem{MatPla06}
\by S.~I.~Matyukevich, B.~A.~Plamenevskii
\paper Elastodynamics in domains with edges
\jour Algebra i Analiz
\yr 2006
\vol 18
\issue 3
\pages 158--233
\mathnet{http://mi.mathnet.ru/aa75}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2255852}
\zmath{https://zbmath.org/?q=an:05236247}
\elib{http://elibrary.ru/item.asp?id=12894793}
\transl
\jour St. Petersburg Math. J.
\yr 2007
\vol 18
\issue 3
\pages 459--510
\crossref{https://doi.org/10.1090/S1061-0022-07-00957-0}


Linking options:
  • http://mi.mathnet.ru/eng/aa75
  • http://mi.mathnet.ru/eng/aa/v18/i3/p158

    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. Hung N.M., Anh C.T., “Asymptotic Expansions of Solutions of the First Initial Boundary-Value Problem for Schrodinger Systems in Domains with Conical Points. II”, Ukrainian Mathematical Journal, 61:12 (2009), 1923–1945  crossref  mathscinet  zmath  isi  scopus
    2. D. V. Korikov, “Asymptotic behavior of solutions to wave equation in domain with a small hole”, St. Petersburg Math. J., 26:5 (2015), 813–838  mathnet  crossref  mathscinet  isi  elib  elib
    3. Vu Trong Luong, Nguyen Thi Hue, “On the Asymptotic of Solution To the Dirichlet Problem For Hyperbolic Equations in Cylinders With Edges”, Electron. J. Qual. Theory Differ., 2014, no. 10, 1–15  crossref  mathscinet  isi
    4. D. V. Korikov, B. A. Plamenevskiǐ, “Asymptotics of solutions for stationary and nonstationary Maxwell systems in a domain with small holes”, St. Petersburg Math. J., 28:4 (2017), 507–554  mathnet  crossref  mathscinet  isi  elib
    5. Mueller F. Schwab Ch., “Finite elements with mesh refinement for elastic wave propagation in polygons”, Math. Meth. Appl. Sci., 39:17 (2016), 5027–5042  crossref  mathscinet  zmath  isi  scopus
    6. Gimperlein H. Meyer F. Oezdemir C. Stark D. Stephan E.P., “Boundary Elements With Mesh Refinements For the Wave Equation”, Numer. Math., 139:4 (2018), 867–912  crossref  mathscinet  zmath  isi  scopus
    7. Mueller F. Schotzau D. Schwab Ch., “Discontinuous Galerkin Methods For Acoustic Wave Propagation in Polygons”, J. Sci. Comput., 77:3, SI (2018), 1909–1935  crossref  mathscinet  zmath  isi  scopus
    8. Korikov D. Plamenevskii B., “Asymptotics of Solutions to Nonstationary Maxwell System in Domains With Small Cavities”, 2018 Days on Diffraction (Dd), ed. Motygin O. Kiselev A. Goray L. Kazakov A. Kirpichnikova A. Perel M., IEEE, 2018, 176–181  crossref  isi
  • Алгебра и анализ St. Petersburg Mathematical Journal
    Number of views:
    This page:331
    Full text:109
    References:39
    First page:4

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