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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

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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
\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
\jour Comput. Math. Math. Phys.
\yr 2017
\vol 57
\issue 5
\pages 854--866

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    Citing articles on Google Scholar: Russian citations, English citations
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    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  mathscinet  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
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