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Mat. Zametki, 1998, Volume 63, Issue 3, Pages 354–362 (Mi mz1289)  

This article is cited in 19 scientific papers (total in 19 papers)

A singularly perturbed boundary value problem for a second-order equation in the case of variation of stability

V. F. Butuzov, N. N. Nefedov

M. V. Lomonosov Moscow State University

Abstract: A boundary value problem for a second-order nonlinear singularly perturbed differential equation is considered for the case in which there is variation of stability caused by the intersection of roots of the degenerate equation. By the method of differential inequalities, we prove the existence of a solution such that the limit solution is nonsmooth.

DOI: https://doi.org/10.4213/mzm1289

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English version:
Mathematical Notes, 1998, 63:3, 311–318

Bibliographic databases:

UDC: 517.956.226
Received: 29.04.1996

Citation: V. F. Butuzov, N. N. Nefedov, “A singularly perturbed boundary value problem for a second-order equation in the case of variation of stability”, Mat. Zametki, 63:3 (1998), 354–362; Math. Notes, 63:3 (1998), 311–318

Citation in format AMSBIB
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\pages 354--362
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\jour Math. Notes
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Butuzov, VF, “Singularly perturbed boundary value problems for systems of Tichonov's type in case of exchange of stabilities”, Journal of Differential Equations, 159:2 (1999), 427  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    2. V. F. Butuzov, E. A. Gromova, “A limit theorem for a Tikhonov system of equations”, Comput. Math. Math. Phys., 40:5 (2000), 669–679  mathnet  mathscinet  zmath
    3. Butuzov, VF, “Singularly perturbed elliptic problems in the case of exchange of stabilities”, Journal of Differential Equations, 169:2 (2001), 373  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    4. V. F. Butuzov, E. A. Gromova, “Boundary value problem for a system of fast and slow second-order equations in the case of intersecting roots of the degenerate equation”, Comput. Math. Math. Phys., 41:8 (2001), 1108–1121  mathnet  mathscinet  zmath
    5. Butuzov, VF, “Singularly perturbed partly dissipative reaction-diffusion systems in case of exchange of stabilities”, Journal of Mathematical Analysis and Applications, 273:1 (2002), 217  crossref  mathscinet  zmath  isi  scopus  scopus
    6. Butuzov, VF, “Singularly perturbed parabolic equation in the case of intersecting roots of the degenerate equation”, Russian Journal of Mathematical Physics, 9:1 (2002), 50  mathscinet  zmath  isi
    7. V. F. Butuzov, N. N. Nefedov, K. R. Schneider, “On a singularly perturbed system of parabolic equations in the case of intersecting roots of the degenerate equation”, Comput. Math. Math. Phys., 42:2 (2002), 176–187  mathnet  mathscinet  zmath  elib
    8. V. F. Butuzov, M. A. Terent'ev, “System of singularly perturbed equations in the case of intersecting roots of a degenerate system”, Comput. Math. Math. Phys., 42:11 (2002), 1622–1635  mathnet  mathscinet  zmath
    9. V. F. Butuzov, E. A. Gromova, “Singularly perturbed parabolic problem in the case of intersecting roots of the degenerate equation”, Proc. Steklov Inst. Math. (Suppl.), 2003no. , suppl. 1, S37–S44  mathnet  mathscinet  zmath  elib
    10. N. N. Nefedov, K. R. Schneider, “Delay of exchange of stabilities in singularly perturbed parabolic problems”, Proc. Steklov Inst. Math. (Suppl.), 2003no. , suppl. 1, S144–S154  mathnet  mathscinet  zmath  elib
    11. Comput. Math. Math. Phys., 44:7 (2004), 1213–1220  mathnet  mathscinet  zmath
    12. A. M. Il'in, S. F. Dolbeeva, “Asymptotics of the solution to a differential equation with a small parameter in the case of two limit solutions”, Proc. Steklov Inst. Math. (Suppl.), 253, suppl. 1 (2006), S105–S116  mathnet  crossref  mathscinet  zmath  elib
    13. Dolbeeva, SF, “Asymptotic behavior of the solution to a differential equation with a small parameter when the stability lines of the limit solution intersect”, Doklady Mathematics, 73:3 (2006), 388  crossref  zmath  isi  elib  scopus  scopus
    14. V. F. Butuzov, “On the stability and domain of attraction of a stationary nonsmooth limit solution of a singularly perturbed parabolic equation”, Comput. Math. Math. Phys., 46:3 (2006), 413–424  mathnet  crossref  mathscinet  zmath
    15. S. F. Dolbeeva, E. A. Chizh, “Asymptotics of a second-order differential equation with a small parameter in the case when the reduced equation has two solutions”, Comput. Math. Math. Phys., 48:1 (2008), 30–42  mathnet  crossref  mathscinet  zmath  isi
    16. Comput. Math. Math. Phys., 48:1 (2008), 43–58  mathnet  crossref  mathscinet  zmath  isi  elib
    17. Kadalbajoo M.K., Gupta V., “A Brief Survey on Numerical Methods for Solving Singularly Perturbed Problems”, Appl. Math. Comput., 217:8 (2010), 3641–3716  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    18. M. A. Terentev, “Ob otsutstvii i razrushenii reshenii v nekotorykh singulyarno vozmuschennykh zadachakh so smenoi ustoichivosti”, Model. i analiz inform. sistem, 23:5 (2016), 587–594  mathnet  crossref  mathscinet  elib
    19. M. A. Terentev, “Zamechanie ob oblasti prityazheniya statsionarnogo resheniya odnogo singulyarno vozmuschennogo parabolicheskogo uravneniya”, Model. i analiz inform. sistem, 24:3 (2017), 353–358  mathnet  crossref  elib
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