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Zh. Vychisl. Mat. Mat. Fiz., 2013, Volume 53, Number 9, Pages 1427–1447 (Mi zvmmf9912)  

This article is cited in 11 scientific papers (total in 11 papers)

A steplike contrast structure in a singularly perturbed system of elliptic equations

V. F. Butuzov, N. T. Levashova, A. A. Mel'nikova

Faculty of Physics, Lomonosov Moscow State University, Moscow, 119992, Russia

Abstract: A singularly perturbed boundary value problem for a system of elliptic equations in a two-dimensional region is considered. The asymptotics and existence of a solution with an internal transition layer are studied. The asymptotics is justified by the method of differential inequalities.

Key words: singularly perturbed system of elliptic equations, small parameter, asymptotic method of solution.

DOI: https://doi.org/10.7868/S0044466913090068

Full text: PDF file (289 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2013, 53:9, 1239–1259

Bibliographic databases:

UDC: 519.624.2
Received: 15.04.2013

Citation: V. F. Butuzov, N. T. Levashova, A. A. Mel'nikova, “A steplike contrast structure in a singularly perturbed system of elliptic equations”, Zh. Vychisl. Mat. Mat. Fiz., 53:9 (2013), 1427–1447; Comput. Math. Math. Phys., 53:9 (2013), 1239–1259

Citation in format AMSBIB
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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, J. V. Muhartova, M. A. Davydova, N. E. Shapkina, A. V. Oltchev, “The application of the theory of contrast structures for describing wind field in spatially heterogeneous vegetation cover”, Mosc. Univ. Phys. Bull., 70:3 (2015), 167–174  crossref  mathscinet  isi  elib  scopus
    2. D. A. Tursunov, U. Z. Erkebaev, “Asimptoticheskoe razlozhenie resheniya zadachi Dirikhle dlya koltsa s osobennostyu na granitse”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2016, no. 1(39), 42–52  mathnet  crossref  elib
    3. Ni Mingkang, Wang Aifeng, Cheng Huaxiong, “Step-like contrast structure for a quasilinear system of singularly perturbed differential equations with a zero characteristic number”, Differ. Equ., 52:2 (2016), 186–196  crossref  mathscinet  zmath  isi  elib  scopus
    4. A. E. Sidorova, N. T. Levashova, A. A. Melnikova, N. N. Deryugina, A. E. Semina, “Autowave self-organization in heterogeneous natural-anthropogenic ecosystems”, Mosc. Univ. Phys. Bull., 71:6 (2016), 562–568  crossref  isi  scopus
    5. E. A. Antipov, V. T. Volkov, N. T. Levashova, N. N. Nefedov, “Reshenie vida dvizhuschegosya fronta dvumernoi zadachi reaktsiya-diffuziya”, Model. i analiz inform. sistem, 24:3 (2017), 259–279  mathnet  crossref  elib
    6. N. T. Levashova, N. N. Nefedov, A. O. Orlov, “Time-independent reaction-diffusion equation with a discontinuous reactive term”, Comput. Math. Math. Phys., 57:5 (2017), 854–866  mathnet  crossref  crossref  mathscinet  isi  elib
    7. N. T. Levashova, A. A. Melnikova, D. V. Lukyanenko, A. E. Sidorova, S. V. Bytsyura, “Modelirovanie urboekosistem kak protsessov samoorganizatsii”, Matem. modelirovanie, 29:11 (2017), 40–52  mathnet  elib
    8. A. E. Sidorova, N. T. Levashova, A. A. Melnikova, A. E. Semina, “Model strukturoobrazovaniya urboekosistem kak protsess avtovolnovoi samoorganizatsii v aktivnykh sredakh”, Matem. biologiya i bioinform., 12:1 (2017), 186–197  mathnet  crossref
    9. A. A. Melnikova, N. N. Derugina, “The dynamics of the autowave front in a model of urban ecosystems”, Mosc. Univ. Phys. Bull., 73:3 (2018), 284–292  crossref  isi  scopus
    10. N. T. Levashova, S. V. Bytsyura, “Verkhnee i nizhnee resheniya dlya sistemy uravnenii tipa FitsKhyu–Nagumo”, Model. i analiz inform. sistem, 25:1 (2018), 33–53  mathnet  crossref  elib
    11. 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
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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