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Zh. Vychisl. Mat. Mat. Fiz., 2012, Volume 52, Number 11, Pages 1983–2003 (Mi zvmmf9751)  

This article is cited in 12 scientific papers (total in 12 papers)

Steplike contrast structure in a singularly perturbed system of equations with different powers of small parameter

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

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

Abstract: A singularly perturbed boundary value problem for a system of equations with different powers of a small parameter is considered in the one-dimensional case. The asymptotic behavior and existence of a solution with an internal transition layer are analyzed. The asymptotics are substantiated using the asymptotic method of differential inequalities.

Key words: singularly perturbed system of second-order differential equations, small parameter, asymptotic solution method.

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English version:
Computational Mathematics and Mathematical Physics, 2012, 52:11, 1526–1546

Bibliographic databases:

UDC: 519.624.2
Received: 22.05.2012

Citation: V. F. Butuzov, N. T. Levashova, A. A. Mel'nikova, “Steplike contrast structure in a singularly perturbed system of equations with different powers of small parameter”, Zh. Vychisl. Mat. Mat. Fiz., 52:11 (2012), 1983–2003; Comput. Math. Math. Phys., 52:11 (2012), 1526–1546

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. 51, no. 3, 2015, 342–361  crossref  mathscinet  zmath  isi  elib  scopus
    2. V. F. Butuzov, N. T. Levashova, A. A. Mel'nikova, “A steplike contrast structure in a singularly perturbed system of elliptic equations”, Comput. Math. Math. Phys., 53:9 (2013), 1239–1259  mathnet  crossref  crossref  isi  elib  elib
    3. N. N. Nefedov, Minkang Ni, “Internal layers in the one-dimensional reactiondiffusion equation with a discontinuous reactive term”, Comput. Math. Math. Phys., 55:12 (2015), 2001–2007  mathnet  crossref  crossref  mathscinet  isi  elib
    4. A. A. Melnikova, R. L. Argun, “Asimptotika statsionarnogo resheniya s vnutrennim perekhodnym sloem dlya sistemy tipa FittsKhyuNagumo”, Model. i analiz inform. sistem, 23:5 (2016), 559–567  mathnet  crossref  mathscinet  elib
    5. 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
    6. 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
    7. 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
    8. 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
    9. A. Melnikova, N. Levashova, D. Lukyanenko, “Front dynamics in an activator-inhibitor system of equations”, Numerical Analysis and Its Applications, NAA 2016, Lecture Notes in Computer Science, 10187, eds. I. Dimov, I. Farago, L. Vulkov, Springer, 2017, 492–499  crossref  mathscinet  zmath  isi  scopus
    10. 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
    11. S. V. Bytsyura, N. T. Levashova, “Verkhnee i nizhnee resheniya dlya sistemy uravnenii tipa FitsKhyu–Nagumo”, Model. i analiz inform. sistem, 25:1 (2018), 33–53  mathnet  crossref  elib
    12. 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
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