RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
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



TMF:
Year:
Volume:
Issue:
Page:
Find






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


TMF, 1999, Volume 119, Number 2, Pages 295–307 (Mi tmf740)  

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

Two physical applications of the Laplace operator perturbed on a null set

I. Yu. Popov, D. A. Zubok

St. Petersburg State University of Information Technologies, Mechanics and Optics

Abstract: Two physical applications of the Laplace operator perturbed on a set of zero measure are suggested. The approach is based on the theory of self-adjoint extensions of symmetrical operators. The first application is a solvable model of scattering of a plane wave by a perturbed thin cylinder. “Nonlocal” extensions are described. The model parameters can be chosen such that the model solution is an approximation of the corresponding “realistic” solution. The second application is the description of the time evolution of a one-dimensional quasi-Chaplygin medium, which can be reduced using a hodograph transform to the ill-posed problem of the Laplace operator perturbed on a set of codimension two in $\mathbf R^3$. Stability and instability conditions are obtained.

DOI: https://doi.org/10.4213/tmf740

Full text: PDF file (265 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 1999, 119:2, 629–639

Bibliographic databases:

Received: 02.09.1998
Revised: 02.11.1998

Citation: I. Yu. Popov, D. A. Zubok, “Two physical applications of the Laplace operator perturbed on a null set”, TMF, 119:2 (1999), 295–307; Theoret. and Math. Phys., 119:2 (1999), 629–639

Citation in format AMSBIB
\Bibitem{PopZub99}
\by I.~Yu.~Popov, D.~A.~Zubok
\paper Two physical applications of the Laplace operator perturbed on a null set
\jour TMF
\yr 1999
\vol 119
\issue 2
\pages 295--307
\mathnet{http://mi.mathnet.ru/tmf740}
\crossref{https://doi.org/10.4213/tmf740}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1718661}
\zmath{https://zbmath.org/?q=an:0944.35016}
\elib{http://elibrary.ru/item.asp?id=13331076}
\transl
\jour Theoret. and Math. Phys.
\yr 1999
\vol 119
\issue 2
\pages 629--639
\crossref{https://doi.org/10.1007/BF02557355}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000081597700005}


Linking options:
  • http://mi.mathnet.ru/eng/tmf740
  • https://doi.org/10.4213/tmf740
  • http://mi.mathnet.ru/eng/tmf/v119/i2/p295

    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. B. E. Kanguzhin, D. B. Nurakhmetov, N. E. Tokmagambetov, “Laplace operator with $\delta$-like potentials”, Russian Math. (Iz. VUZ), 58:2 (2014), 6–12  mathnet  crossref
    2. Nalzhupbayeva G., “Formulas For the Eigenvalues of the Iterated Laplacian With Singular Potentials”, International Conference Functional Analysis in Interdisciplinary Applications (FAIA2017), AIP Conference Proceedings, 1880, eds. Kalmenov T., Sadybekov M., Amer Inst Physics, 2017, UNSP 050005  crossref  isi  scopus  scopus  scopus
    3. Nalzhupbayeva G., “Remark on the Eigenvalues of the M-Laplacian in a Punctured Domain”, Complex Anal. Oper. Theory, 12:3 (2018), 599–606  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    4. Nalzhupbayeva G., “Spectral Properties of One Elliptic Operator in a Punctured Domain”, AIP Conference Proceedings, 1997, eds. Ashyralyev A., Lukashov A., Sadybekov M., Amer Inst Physics, 2018, UNSP 020083-1  crossref  isi  scopus
    5. Nalzhupbayeva G., “Spectral Properties of the Iterated Laplacian With a Potential in a Punctured Domain”, Filomat, 32:8 (2018), 2897–2900  crossref  mathscinet  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
    Number of views:
    This page:283
    Full text:89
    References:35
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020