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Mat. Zametki, 2013, Volume 94, Issue 1, Pages 68–80 (Mi mz10106)  

This article is cited in 24 scientific papers (total in 24 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

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.

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

Full text: PDF file (457 kB)
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English version:
Mathematical Notes, 2013, 94:1, 60–70

Bibliographic databases:

UDC: 517.228.4
Received: 21.07.2012
Revised: 26.12.2012

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

    This publication is cited in the following articles:
    1. V. A. Beloshapko, V. F. Butuzov, “A singularly perturbed elliptic problem in the case of a multiple root of the degenerate equation”, Comput. Math. Math. Phys., 53:8 (2013), 1117–1127  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    2. V. F. Butuzov, “Asymptotics of the solution of a system of singularly perturbed equations in the case of a multiple root of the degenerate equation”, Differ. Equ., 50:2 (2014), 177–188  crossref  mathscinet  zmath  isi  elib  elib  scopus
    3. M. V. Butuzova, “The Cauchy problem for Tikhonovs system in the case of a multiple root of the degenerate equation”, Comput. Math. Math. Phys., 55:1 (2015), 31–42  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    4. V. F. Butuzov, “Singularly perturbed boundary value problem with multizonal interior transitional layer”, Automatic Control and Computer Sciences, 49:7 (2015), 493–507  mathnet  crossref  mathscinet  isi  elib  elib
    5. V. F. Butuzov, A. I. Bychkov, “Nachalno-kraevaya zadacha dlya singulyarno vozmuschennogo parabolicheskogo uravneniya v sluchayakh dvukratnogo i trekhkratnogo kornya vyrozhdennogo uravneniya”, Chebyshevskii sb., 16:4 (2015), 41–76  mathnet  elib
    6. Butuzov V.F., “On the stability and the attraction domain of the stationary solution of a singularly perturbed parabolic equation with a multiple root of the degenerate equation”, Differ. Equ., 51:12 (2015), 1569–1582  crossref  mathscinet  zmath  isi  elib  scopus
    7. V. F. Butuzov, “On the Dependence of the Structure of Boundary Layers on the Boundary Conditions in a Singularly Perturbed Boundary-Value Problem with Multiple Root of the Related Degenerate Equation”, Math. Notes, 99:2 (2016), 210–221  mathnet  crossref  crossref  mathscinet  isi  elib
    8. S. A. Kordyukova, L. A. Kalyakin, “On a double boundary layer in a nonlinear boundary value problem”, Proc. Steklov Inst. Math. (Suppl.), 297, suppl. 1 (2017), 129–146  mathnet  crossref  mathscinet  isi  elib
    9. V. F. Butuzov, “Asymptotic behaviour of the solution to a singularly perturbed partially dissipative system with a multiple root of the degenerate equation”, Sb. Math., 207:8 (2016), 1100–1126  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    10. V. A. Beloshapko, V. F. Butuzov, “Asymptotics of the solution to a singularly perturbed elliptic problem with a three-zone boundary layer”, Comput. Math. Math. Phys., 56:8 (2016), 1414–1425  mathnet  crossref  crossref  isi  elib
    11. V. F. Butuzov, V. A. Beloshapko, “Singulyarno vozmuschennaya ellipticheskaya zadacha Dirikhle s kratnym kornem vyrozhdennogo uravneniya”, Model. i analiz inform. sistem, 23:5 (2016), 515–528  mathnet  crossref  mathscinet  elib
    12. V. F. Butuzov, “Asymptotic behaviour and stability of solutions of a singularly perturbed elliptic problem with a triple root of the degenerate equation”, Izv. Math., 81:3 (2017), 481–504  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    13. V. A. Beloshapko, “Cingulyarno vozmuschennaya ellipticheskaya zadacha Dirikhle s trekhzonnym pogranichnym sloem”, Model. i analiz inform. sistem, 24:3 (2017), 280–287  mathnet  crossref  elib
    14. V. F. Butuzov, “O kontrastnykh strukturakh s mnogozonnym vnutrennim sloem”, Model. i analiz inform. sistem, 24:3 (2017), 288–308  mathnet  crossref  elib
    15. A. A. Bykov, K. E. Ermakova, “Resheniya uravnenii nestatsionarnogo fronta reaktsii s vyrozhdennymi tochkami ravnovesiya”, Model. i analiz inform. sistem, 24:3 (2017), 309–321  mathnet  crossref  elib
    16. V. Beloshapko, “Special properties of the stationary solution for two-dimensional singularly perturbed parabolic problem, stability, and attraction domain”, Math. Meth. Appl. Sci., 41:18, SI (2018), 9264–9275  crossref  mathscinet  zmath  isi  scopus
    17. V. F. Butuzov, “On asymptotics for the solution of a singularly perturbed parabolic problem with a multizone internal transition layer”, Comput. Math. Math. Phys., 58:6 (2018), 925–949  mathnet  crossref  crossref  isi  elib
    18. Comput. Math. Math. Phys., 58:12 (2018), 1989–2001  mathnet  crossref  isi  elib
    19. V. F. Butuzov, “Contrast structures with a multizone internal layer”, Autom. Control Comp. Sci., 52:7 (2018), 745–761  crossref  isi  scopus
    20. 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  adsnasa  isi  elib
    21. 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
    22. 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
    23. 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  isi  elib
    24. V. F. Butuzov, “Singularly perturbed partially dissipative systems of equations”, Theoret. and Math. Phys., 207:2 (2021), 579–593  mathnet  crossref  crossref  isi
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