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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2018, Volume 58, Number 6, Pages 961–987
DOI: https://doi.org/10.7868/S0044466918060108
(Mi zvmmf10708)
 

This article is cited in 7 scientific papers (total in 7 papers)

On asymptotics for the solution of a singularly perturbed parabolic problem with a multizone internal transition layer

V. F. Butuzov

Department of Physics, Moscow State University, Moscow, Russia
Citations (7)
References:
Abstract: For a singularly perturbed parabolic equation with Neumann boundary conditions, we construct and substantiate asymptotics of a time-periodic solution possessing a multizone internal transition layer. Multizonality of the transition layer is caused by the fact that the degenerate equation has three nonintersecting roots, two of which are simple and the third one has multiplicity two. The asymptotic decomposition of the solution is qualitatively different from the well-known decomposition in the case when all the three roots of the degenerate equation are simple.
Key words: parabolic problem, internal transition layer, asymptotic solution, steplike contrast structure.
Funding agency Grant number
Russian Science Foundation 18-11-00042
Received: 05.11.2017
English version:
Computational Mathematics and Mathematical Physics, 2018, Volume 58, Issue 6, Pages 925–949
DOI: https://doi.org/10.1134/S0965542518060040
Bibliographic databases:
Document Type: Article
UDC: 519.633
Language: Russian
Citation: V. F. Butuzov, “On asymptotics for the solution of a singularly perturbed parabolic problem with a multizone internal transition layer”, Zh. Vychisl. Mat. Mat. Fiz., 58:6 (2018), 961–987; Comput. Math. Math. Phys., 58:6 (2018), 925–949
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/zvmmf10708
  • https://www.mathnet.ru/eng/zvmmf/v58/i6/p961
  • This publication is cited in the following 7 articles:
    1. G. A. Kurina, M. A. Kalashnikova, “Singularly perturbed problems with multi-tempo fast variables”, Autom. Remote Control, 83:11 (2022), 1679–1723  mathnet  crossref  crossref
    2. Galina Bizhanova, “Solution of the nonregular problem for a parabolic equation with the time derivative in the boundary condition”, ASY, 130:1-2 (2022), 53  crossref
    3. M. V. Butuzova, “Asymptotics of the solution of a Tikhonov system of equations with a multizone boundary layer”, Comput. Math. Math. Phys., 62:6 (2022), 863–883  mathnet  mathnet  crossref  crossref
    4. D. A. Tursunov, K. G. Kozhobekov, A. A. Shoorukov, “Asymptotics of the Solution of Bisingularly Perturbed First Boundary Value Problem”, Lobachevskii J Math, 43:2 (2022), 506  crossref
    5. V. F. Butuzov, “Asymptotics of a steplike contrast structure in a partially dissipative stationary system of equations”, Comput. Math. Math. Phys., 61:1 (2021), 53–79  mathnet  crossref  crossref  isi  elib
    6. N. N. Nefedov, “Development of methods of asymptotic analysis of transition layers in reaction–diffusion–advection equations: theory and applications”, Comput. Math. Math. Phys., 61:12 (2021), 2068–2087  mathnet  mathnet  crossref  crossref  isi  scopus
    7. D. A. Tursunov, M. O. Orozov, A. A. Halmatov, “Asymptotics of the solution to the boundary-value problems with non smooth coefficient”, Lobachevskii J. Math., 41:6, SI (2020), 1115–1122  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
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