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., 2017, Volume 57, Number 5, Pages 854–866 (Mi zvmmf10575)  

This article is cited in 9 scientific papers (total in 9 papers)

Time-independent reaction-diffusion equation with a discontinuous reactive term

N. T. Levashova, N. N. Nefedov, A. O. Orlov

Faculty of Physics, Moscow State University, Moscow, Russia

Abstract: A two-dimensional singularly perturbed elliptic equation referred to in applications as the reaction-diffusion equation is considered. The nonlinearity describing the reaction is assumed to be discontinuous on a certain closed curve. On the basis of the generalized asymptotic comparison principle, the existence of smooth solution is proven and the accuracy of the asymptotic approximation is estimated.

Key words: elliptic reaction-diffusion problem, boundary layers, asymptotics of solution, estimation of accuracy.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00437_a


DOI: https://doi.org/10.7868/S0044466917050064

Full text: PDF file (499 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2017, 57:5, 854–866

Bibliographic databases:

UDC: 519.633
Received: 03.02.2016

Citation: N. T. Levashova, N. N. Nefedov, A. O. Orlov, “Time-independent reaction-diffusion equation with a discontinuous reactive term”, Zh. Vychisl. Mat. Mat. Fiz., 57:5 (2017), 854–866; Comput. Math. Math. Phys., 57:5 (2017), 854–866

Citation in format AMSBIB
\Bibitem{LevNefOrl17}
\by N.~T.~Levashova, N.~N.~Nefedov, A.~O.~Orlov
\paper Time-independent reaction-diffusion equation with a discontinuous reactive term
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2017
\vol 57
\issue 5
\pages 854--866
\mathnet{http://mi.mathnet.ru/zvmmf10575}
\crossref{https://doi.org/10.7868/S0044466917050064}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3661121}
\elib{http://elibrary.ru/item.asp?id=29331738}
\transl
\jour Comput. Math. Math. Phys.
\yr 2017
\vol 57
\issue 5
\pages 854--866
\crossref{https://doi.org/10.1134/S0965542517050062}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000403459000008}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85020685393}


Linking options:
  • http://mi.mathnet.ru/eng/zvmmf10575
  • http://mi.mathnet.ru/eng/zvmmf/v57/i5/p854

    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. N. T. Levashova, O. A. Nikolaeva, “Asimptoticheskoe issledovanie resheniya uravneniya teploprovodnosti vblizi granitsy razdela dvukh sred”, Model. i analiz inform. sistem, 24:3 (2017), 339–352  mathnet  crossref  elib
    2. Ni M., Pang Ya., Levashova N.T., Nikolaeva O.A., “Internal Layers For a Singularly Perturbed Second-Order Quasilinear Differential Equation With Discontinuous Right-Hand Side”, Differ. Equ., 53:12 (2017), 1567–1577  crossref  mathscinet  zmath  isi
    3. A. O. Orlov, N. T. Levashova, N. N. Nefedov, “Solution of contrast structure type for a parabolic reaction-diffusion problem in a medium with discontinuous characteristics”, Differ. Equ., 54:5 (2018), 669–686  crossref  mathscinet  isi
    4. A. A. Melnikova, N. N. Deryugina, “Periodicheskie izmeneniya avtovolnovogo fronta v dvumernoi sisteme parabolicheskikh uravnenii”, Model. i analiz inform. sistem, 25:1 (2018), 112–124  mathnet  crossref  elib
    5. Yafei Pan, Min Kan Ni, M. A. Davydova, “Contrast Structures in Problems for a Stationary Equation of Reaction-Diffusion-Advection Type with Discontinuous Nonlinearity”, Math. Notes, 104:5 (2018), 735–744  mathnet  crossref  crossref  isi  elib
    6. Pang Yafei, Ni Mingkang, N. T. Levashova, “Internal layer for a system of singularly perturbed equations with discontinuous right-hand side”, Differ. Equ., 54:12 (2018), 1583–1594  crossref  mathscinet  isi  scopus
    7. N. N. Nefedov, N. T. Levashova, A. O. Orlov, “The asymptotic stability of a stationary solution with an internal transition layer to a reaction-diffusion problem with a discontinuous reactive term”, Mosc. Univ. Phys. Bull., 73:6 (2018), 565–572  crossref  mathscinet  isi  scopus
    8. A. E. Sidorova, N. T. Levashova, A. E. Semina, A. A. Melnikova, “The application of a distributed model of active media for the analysis of urban ecosystems development”, Matem. biologiya i bioinform., 13:2 (2018), 454–465  mathnet  crossref
    9. Qi X., Ni M., “On the Asymptotic Solution to a Type of Piecewise-Continuous Second-Order Dirichlet Problems of Tikhonov System”, J. Appl. Anal. Comput., 9:1 (2019), 105–117  crossref  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
    Number of views:
    This page:142
    References:28
    First page:26

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