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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2011, Volume 51, Number 1, Pages 44–55 (Mi zvmmf8045)  

This article is cited in 22 scientific papers (total in 22 papers)

On periodic solutions to singularly perturbed parabolic problems in the case of multiple roots of the degenerate equation

V. F. Butuzov

Faculty of Physics, Moscow State University, Moscow, 119992 Russia
References:
Abstract: For singularly perturbed parabolic problems, asymptotic expansions of time-periodic solutions with boundary layers in a neighborhood of interval's endpoints are constructed and justified in the case where the degenerate equation has a double or a triple root.
Key words: singularly perturbed parabolic equations, asymptotic boundary layer, multiple roots of the degenerate equation.
Received: 23.06.2010
English version:
Computational Mathematics and Mathematical Physics, 2011, Volume 51, Issue 1, Pages 40–50
DOI: https://doi.org/10.1134/S0965542511010064
Bibliographic databases:
Document Type: Article
UDC: 519.633
Language: Russian
Citation: V. F. Butuzov, “On periodic solutions to singularly perturbed parabolic problems in the case of multiple roots of the degenerate equation”, Zh. Vychisl. Mat. Mat. Fiz., 51:1 (2011), 44–55; Comput. Math. Math. Phys., 51:1 (2011), 40–50
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/zvmmf8045
  • https://www.mathnet.ru/eng/zvmmf/v51/i1/p44
  • This publication is cited in the following 22 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
    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. 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
    6. 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
    7. 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
    8. 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
    9. A. A. Bykov, K. E. Ermakova, “Nonstationary contrast structures of the problem of reaction-diffusion with roots of integral sheet in a inhomogeneous medium”, Math. Models Comput. Simul., 12:3 (2020), 329–347  mathnet  crossref  crossref  elib
    10. 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  isi
    11. 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
    12. A. A. Bykov, K. E. Ermakova, “Exact solutions of equations of a nonstationary front with equilibrium points of a fractional order”, Comput. Math. Math. Phys., 58:12 (2018), 1977–1988  mathnet  crossref  crossref  isi  elib
    13. Comput. Math. Math. Phys., 58:12 (2018), 1989–2001  mathnet  crossref  isi  elib
    14. Bykov A.A. Ermakova K.E., “Exact Solutions of the Equations of a Nonstationary Front With Equilibrium Points of An Infinite Order of Degeneracy”, Mosc. Univ. Phys. Bull., 73:6 (2018), 583–591  crossref  mathscinet  isi
    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. Butuzov V.F., Nefedov N.N., Recke L., Schneider K.R., “Asymptotics, Stability, and Region of Attraction of Periodic Solution to a Singularly Perturbed Parabolic Problem With Double Root of a Degenerate Equation”, Autom. Control Comp. Sci., 51:7 (2017), 606–613  crossref  mathscinet  isi  scopus
    17. V. F. Butuzov, N. N. Nefedov, L. Recke, K. Schneider, “Asymptotics, stability and region of attraction of a periodic solution to a singularly perturbed parabolic problem in case of a multiple root of the degenerate equation”, Automatic Control and Computer Sciences, 51:7 (2017), 606–613  mathnet  crossref  crossref  mathscinet  elib
    18. 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
    19. 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
    20. V. F. Butuzov, “On the Special Properties of the Boundary Layer in Singularly Perturbed Problems with Multiple Root of the Degenerate Equation”, Math. Notes, 94:1 (2013), 60–70  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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