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

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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

Full-text PDF (457 kB) Citations (39)

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DOI: https://doi.org/10.4213/mzm10106

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

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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:

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
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
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
G. A. Kurina, M. A. Kalashnikova, “Singularly perturbed problems with multi-tempo fast variables”, Autom. Remote Control, 83:11 (2022), 1679–1723
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
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
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
V. F. Butuzov, “Singularly perturbed partially dissipative systems of equations”, Theoret. and Math. Phys., 207:2 (2021), 579–593
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
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
Assiya Zhumanazarova, Young Im Cho, 2021 International Conference on Information and Communication Technology Convergence (ICTC), 2021, 477
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
V. F. Butuzov, “On singularly perturbed systems of ODE with a multiple root of the degenerate equation”, Izv. Math., 84:2 (2020), 262–290
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
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
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
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
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
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
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

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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