RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Guidelines for authors
Publishing Ethics

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



CMFD:
Year:
Volume:
Issue:
Page:
Find






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


CMFD, 2011, Volume 39, Pages 173–184 (Mi cmfd180)  

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

Averaging of boundary-value problems for the Laplace operator in perforated domains with a nonlinear boundary condition of the third type on the boundary of cavities

M. N. Zubovaa, T. A. Shaposhnikovab

a Moscow
b Moscow State University, Moscow, Russia

Abstract: In this paper, the asymptotic behavior of solutions $u_\varepsilon$ of the Poisson equation in the $\varepsilon$-periodically perforated domain $\Omega_\varepsilon\subset\mathbb R^n$, $n\ge3$, with the third nonlinear boundary condition of the form $\partial_\nu u_\varepsilon+\varepsilon^{-\gamma}\sigma(x,u_\varepsilon)=\varepsilon^{-\gamma}g(x)$ on a boundary of cavities, is studied. It is supposed that the diameter of cavities has the order $\varepsilon^\alpha$ with $\alpha>1$ and any $\gamma$. Here, all types of asymptotic behavior of solutions $u_\varepsilon$, corresponding to different relations between parameters $\alpha$ and $\gamma$, are studied.

Full text: PDF file (163 kB)
References: PDF file   HTML file

English version:
Journal of Mathematical Sciences, 2013, 190:1, 181–193

Bibliographic databases:

UDC: 517.9

Citation: M. N. Zubova, T. A. Shaposhnikova, “Averaging of boundary-value problems for the Laplace operator in perforated domains with a nonlinear boundary condition of the third type on the boundary of cavities”, Partial differential equations, CMFD, 39, PFUR, M., 2011, 173–184; Journal of Mathematical Sciences, 190:1 (2013), 181–193

Citation in format AMSBIB
\Bibitem{ZubSha11}
\by M.~N.~Zubova, T.~A.~Shaposhnikova
\paper Averaging of boundary-value problems for the Laplace operator in perforated domains with a~nonlinear boundary condition of the third type on the boundary of cavities
\inbook Partial differential equations
\serial CMFD
\yr 2011
\vol 39
\pages 173--184
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd180}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2830684}
\transl
\jour Journal of Mathematical Sciences
\yr 2013
\vol 190
\issue 1
\pages 181--193
\crossref{https://doi.org/10.1007/s10958-013-1253-5}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84874950023}


Linking options:
  • http://mi.mathnet.ru/eng/cmfd180
  • http://mi.mathnet.ru/eng/cmfd/v39/p173

    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. Ildefonso Diaz J., Gomez-Castro D., Podol'skii V A., Shaposhnikova T.A., “Characterizing the Strange Term in Critical Size Homogenization: Quasilinear Equations With a General Microscopic Boundary Condition”, Adv. Nonlinear Anal., 8:1 (2019), 679–693  crossref  mathscinet  zmath  isi  scopus
  • Современная математика. Фундаментальные направления
    Number of views:
    This page:458
    Full text:140
    References:23

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2021