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Matematicheskie Zametki, 2013, Volume 94, Issue 1, Pages 68–80
DOI: https://doi.org/10.4213/mzm10106
(Mi mzm10106)
 

This article is cited in 39 scientific papers (total in 39 papers)

On the Special Properties of the Boundary Layer in Singularly Perturbed Problems with Multiple Root of the Degenerate Equation

V. F. Butuzov

M. V. Lomonosov Moscow State University
References:
Abstract: Using the boundary-value problem for the singularly perturbed second-order differential equation as an example, we show that the multiplicity of the root of the degenerate equation significantly affects the asymptotics of the solution, especially in the boundary layer.
Keywords: singularly perturbed problem, second-order differential equation, boundary layer, boundary layer series.
Received: 21.07.2012
Revised: 26.12.2012
English version:
Mathematical Notes, 2013, Volume 94, Issue 1, Pages 60–70
DOI: https://doi.org/10.1134/S0001434613070067
Bibliographic databases:
Document Type: Article
UDC: 517.228.4
Language: Russian
Citation: V. F. Butuzov, “On the Special Properties of the Boundary Layer in Singularly Perturbed Problems with Multiple Root of the Degenerate Equation”, Mat. Zametki, 94:1 (2013), 68–80; Math. Notes, 94:1 (2013), 60–70
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/mzm10106
  • https://doi.org/10.4213/mzm10106
  • https://www.mathnet.ru/eng/mzm/v94/i1/p68
  • This publication is cited in the following 39 articles:
    1. Qian Yang, Mingkang Ni, “Multizonal Internal Layers in a Stationary Piecewise–Smooth Reaction-Diffusion Equation in the Case of the Difference of Multiplicity for the Roots of the Degenerate Solution”, Comput. Math. and Math. Phys., 64:5 (2024), 1130  crossref
    2. Qian Yang, Mingkang Ni, “Multiscale study on a class of singularly perturbed system with discontinuous right-hand side and multiple root of the degenerate solution”, Communications in Nonlinear Science and Numerical Simulation, 139 (2024), 108247  crossref
    3. Yang Q., Ni M., “Asymptotics of the Solution to a Stationary Piecewise-Smooth Reaction-Diffusion Equation With a Multiple Root of the Degenerate Equation”, Sci. China-Math., 65:2 (2022), 291–308  crossref  mathscinet  isi  scopus
    4. 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
    5. Q. Yang, M. Ni, “Multizonal boundary and internal layers in the singularly perturbed problems for a stationary equation of reaction–advection–diffusion type with weak and discontinuous nonlinearity”, Comput. Math. Math. Phys., 62:12 (2022), 2123–2138  mathnet  mathnet  crossref  crossref
    6. Qian Yang, Mingkang Ni, “ASYMPTOTICS OF A MULTIZONAL INTERNAL LAYER SOLUTION TO A PIECEWISE-SMOOTH SINGULARLY PERTURBED EQUATION WITH A TRIPLE ROOT OF THE DEGENERATE EQUATION”, jaac, 12:6 (2022), 2441  crossref
    7. 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
    8. V. F. Butuzov, “Singularly perturbed partially dissipative systems of equations”, Theoret. and Math. Phys., 207:2 (2021), 579–593  mathnet  crossref  crossref  adsnasa  isi
    9. Samoilenko A.M., Samusenko P.F., “Asymptotic Integration of Singularly Perturbed Differential Algebraic Equations With Turning Points. Part i”, Ukr. Math. J., 72:12 (2021), 1928–1943  crossref  mathscinet  isi
    10. Butuzov V.F., Simakov R.E., “Asymptotics of the Solution of a Singularly Perturbed System of Equations With a Multizone Internal Layer”, Differ. Equ., 57:4 (2021), 415–445  crossref  mathscinet  isi  scopus
    11. Assiya Zhumanazarova, Young Im Cho, 2021 International Conference on Information and Communication Technology Convergence (ICTC), 2021, 477  crossref
    12. Mingkang Ni, Qian Yang, “Multizonal internal layers in the singularly perturbed equation with a discontinuous right-hand side”, Comput. Math. Math. Phys., 61:6 (2021), 953–963  mathnet  mathnet  crossref  crossref  isi  scopus
    13. V. F. Butuzov, “On singularly perturbed systems of ODE with a multiple root of the degenerate equation”, Izv. Math., 84:2 (2020), 262–290  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    14. V. F. Butuzov, “Asymptotic behaviour of a boundary layer solution to a stationary partly dissipative system with a multiple root of the degenerate equation”, Sb. Math., 210:11 (2019), 1581–1608  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    15. Butuzov V.F., “Asymptotics of a Spike Type Contrast Structure in a Problem With a Multiple Root of the Degenerate Equation”, Differ. Equ., 55:6 (2019), 758–775  crossref  mathscinet  isi
    16. Butuzov V.F. Nefedov N.N. Omel'chenko O.E. Recke L., Vii International Conference Problems of Mathematical Physics and Mathematical Modelling, Journal of Physics Conference Series, 1205, IOP Publishing Ltd, 2019  crossref  isi
    17. V. F. Butuzov, “Asymptotic behavior and stability of a stationary boundary-layer solution to a partially dissipative system of equations”, Comput. Math. Math. Phys., 59:7 (2019), 1148–1171  mathnet  crossref  crossref  isi  elib
    18. V. F. Butuzov, “Asymptotic expansion of the solution to a partially dissipative system of equations with a multizone boundary layer”, Comput. Math. Math. Phys., 59:10 (2019), 1672–1692  mathnet  crossref  crossref  isi  elib
    19. V. F. Butuzov, “On One Singularly Perturbed System of Ordinary Differential Equations with Multiple Root of the Degenerate Equation”, J Math Sci, 240:3 (2019), 224  crossref
    20. Vera Beloshapko, “Elimination of the boundary condition singularity. A new approach to solving a system of nonlinear two-dimensional singularly perturbed differential equations”, J. Phys.: Conf. Ser., 1334:1 (2019), 012015  crossref
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