RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Zh. Vychisl. Mat. Mat. Fiz.:
Year:
Volume:
Issue:
Page:
Find






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


Zh. Vychisl. Mat. Mat. Fiz., 2016, Volume 56, Number 11, Pages 1902–1930 (Mi zvmmf10488)  

Convergence of a family of solutions to a Fujita-type equation in domains with cavities

S. V. Pikulin

Dorodnicyn Computing Center, Federal Research Center "Computer Science and Control", Russian Academy of Sciences, Moscow, Russia

Abstract: The Dirichlet problem for a Fujita-type equation, i.e., a second-order quasilinear uniformly elliptic equation is considered in domains $\Omega_\varepsilon$ with spherical or cylindrical cavities of characteristic size $\varepsilon$. The form of the function in the condition on the cavities' boundaries depends on $\varepsilon$. For $\varepsilon$ tending to zero and the number of cavities increasing simultaneously, sufficient conditions are established for the convergence of the family of solutions $\{u_\varepsilon(x)\}$ of this problem to the solution $u(x)$ of a similar problem in the domain $\Omega$ with no cavities with the same boundary conditions imposed on the common part of the boundaries $\partial\Omega$ and $\partial\Omega_\varepsilon$. Convergence rate estimates are given.

Key words: convergence of a family of solutions, nonlinear Fujita-type equation, domains with spherical or cylindrical cavities, convergence rate estimates for solutions.

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-00923_а
Russian Academy of Sciences - Federal Agency for Scientific Organizations 3


DOI: https://doi.org/10.7868/S0044466916110119

Full text: PDF file (474 kB)
References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2016, 56:11, 1872–1900

Bibliographic databases:

UDC: 519.63
Received: 25.12.2015

Citation: S. V. Pikulin, “Convergence of a family of solutions to a Fujita-type equation in domains with cavities”, Zh. Vychisl. Mat. Mat. Fiz., 56:11 (2016), 1902–1930; Comput. Math. Math. Phys., 56:11 (2016), 1872–1900

Citation in format AMSBIB
\Bibitem{Pik16}
\by S.~V.~Pikulin
\paper Convergence of a family of solutions to a Fujita-type equation in domains with cavities
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2016
\vol 56
\issue 11
\pages 1902--1930
\mathnet{http://mi.mathnet.ru/zvmmf10488}
\crossref{https://doi.org/10.7868/S0044466916110119}
\elib{https://elibrary.ru/item.asp?id=27148427}
\transl
\jour Comput. Math. Math. Phys.
\yr 2016
\vol 56
\issue 11
\pages 1872--1900
\crossref{https://doi.org/10.1134/S0965542516110099}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000389803600005}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85000415071}


Linking options:
  • http://mi.mathnet.ru/eng/zvmmf10488
  • http://mi.mathnet.ru/eng/zvmmf/v56/i11/p1902

    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
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
    Number of views:
    This page:147
    Full text:21
    References:34
    First page:7

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