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Differ. Uravn., 1995, Volume 31, Number 7, Pages 1142–1149 (Mi de9455)  

This article is cited in 28 scientific papers (total in 28 papers)

Partial Differential Equations

The method of differential inequalities for some classes of nonlinear singularly perturbed problems with internal layers

N. N. Nefedov

Lomonosov Moscow State University

Full text: PDF file (1522 kB)

English version:
Differential Equations, 1995, 31:7, 1077–1085

Bibliographic databases:
UDC: 517.95
Received: 22.02.1995

Citation: N. N. Nefedov, “The method of differential inequalities for some classes of nonlinear singularly perturbed problems with internal layers”, Differ. Uravn., 31:7 (1995), 1142–1149; Differ. Equ., 31:7 (1995), 1077–1085

Citation in format AMSBIB
\Bibitem{Nef95}
\by N.~N.~Nefedov
\paper The method of differential inequalities for some classes of nonlinear singularly perturbed problems with internal layers
\jour Differ. Uravn.
\yr 1995
\vol 31
\issue 7
\pages 1142--1149
\mathnet{http://mi.mathnet.ru/de9455}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1429769}
\zmath{https://zbmath.org/?q=an:0864.35011}
\transl
\jour Differ. Equ.
\yr 1995
\vol 31
\issue 7
\pages 1077--1085


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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. A. B. Vasil'eva, A. P. Petrov, A. A. Plotnicov, “On the theory of alternating contrast structures”, Comput. Math. Math. Phys., 38:9 (1998), 1471–1480  mathnet  mathscinet  zmath
    2. V. F. Butuzov, I. V. Nedelko, “Existence, local uniqueness, and asymptotics of two-dimensional periodic steplike contrast structures”, Comput. Math. Math. Phys., 39:5 (1999), 779–798  mathnet  mathscinet  zmath
    3. V. F. Butuzov, I. V. Nedelko, “A steplike contrast structure in a singularly perturbed system of elliptic equations with different power of a small parameter”, Comput. Math. Math. Phys., 40:6 (2000), 837–859  mathnet  mathscinet  zmath  elib
    4. I. V. Nedelko, “Asymptotic Stability, Local Uniqueness, and Domain of Attraction of Two-Dimensional Step Type Contrast Structures”, Math. Notes, 69:1 (2001), 72–80  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. V. F. Butuzov, I. V. Nedelko, “Global influence domains of stable solutions with internal layers”, Sb. Math., 192:5 (2001), 651–691  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. N. N. Nefëdov, A. G. Nikitin, “Development of the asymptotic method of differential inequalities for step-type solutions of singularly perturbed integro-differential equations”, Comput. Math. Math. Phys., 41:7 (2001), 1005–1014  mathnet  mathscinet  zmath
    7. V. F. Butuzov, I. V. Nedelko, “On the global domain of influence of stable solutions with interior layers in the two-dimensional case”, Izv. Math., 66:1 (2002), 1–40  mathnet  crossref  crossref  mathscinet  zmath  elib
    8. A. M. Ilin, B. I. Suleimanov, “Koeffitsienty vnutrennego razlozheniya pri issledovanii asimptotiki nekotorykh singulyarnykh kraevykh zadach”, Dalnevost. matem. zhurn., 4:1 (2003), 78–85  mathnet
    9. A. M. Il'in, B. I. Suleimanov, “Birth of step-like contrast structures connected with a cusp catastrophe”, Sb. Math., 195:12 (2004), 1727–1746  mathnet  crossref  crossref  mathscinet  zmath  isi
    10. Comput. Math. Math. Phys., 45:1 (2005), 37–51  mathnet  mathscinet  zmath
    11. I. V. Nedelko, “Existence of solutions with interior transition layers touching the boundary”, Math. Notes, 77:1 (2005), 72–83  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    12. V. T. Volkov, N. N. Nefedov, “Development of the asymptotic method of differential inequalities for investigation of periodic contrast structures in reaction-diffusion equations”, Comput. Math. Math. Phys., 46:4 (2006), 585–593  mathnet  crossref  mathscinet  zmath
    13. N. N. Nefedov, A. G. Nikitin, T. A. Urazgil'dina, “The Cauchy problem for a singularly perturbed Volterra integro-differential equation”, Comput. Math. Math. Phys., 46:5 (2006), 768–775  mathnet  crossref  mathscinet
    14. N. N. Nefedov, A. G. Nikitin, “The Cauchy problem for a singularly perturbed integro-differential Fredholm equation”, Comput. Math. Math. Phys., 47:4 (2007), 629–637  mathnet  crossref  mathscinet  zmath
    15. Comput. Math. Math. Phys., 48:1 (2008), 43–58  mathnet  crossref  mathscinet  zmath  isi  elib
    16. I. V. Nedelko, “Solutions of a problem of ‘reaction–diffusion’ type with internal transition layers in the case of non-linearity of quadratic type”, Izv. Math., 73:1 (2009), 151–170  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    17. A. B. Vasil'eva, “Two-point boundary value problem for a singularly perturbed equation with a reduced equation having multiple roots”, Comput. Math. Math. Phys., 49:6 (2009), 1021–1032  mathnet  crossref  zmath  isi
    18. Yu. V. Bozhevol'nov, N. N. Nefëdov, “Front motion in a parabolic reaction-diffusion problem”, Comput. Math. Math. Phys., 50:2 (2010), 264–273  mathnet  crossref  mathscinet  adsnasa  isi
    19. A. B. Vasil'eva, V. F. Butuzov, N. N. Nefedov, “Singularly perturbed problems with boundary and internal layers”, Proc. Steklov Inst. Math., 268 (2010), 258–273  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    20. N. N. Nefedov, “Obschaya skhema asimptoticheskogo issledovaniya ustoichivykh kontrastnykh struktur”, Nelineinaya dinam., 6:1 (2010), 181–186  mathnet
    21. V. F. Butuzov, N. T. Levashova, A. A. Mel'nikova, “Steplike contrast structure in a singularly perturbed system of equations with different powers of small parameter”, Comput. Math. Math. Phys., 52:11 (2012), 1526–1546  mathnet  crossref  mathscinet  isi  elib  elib
    22. N. N. Nefedov, A. G. Nikitin, “The initial boundary value problem for a nonlocal singularly perturbed reaction–diffusion equation”, Comput. Math. Math. Phys., 52:6 (2012), 926–931  mathnet  crossref  mathscinet  adsnasa  isi  elib  elib
    23. N. T. Levashova, N. N. Nefedov, A. V. Yagremtsev, “Contrast structures in the reaction-diffusion-advection equations in the case of balanced advection”, Comput. Math. Math. Phys., 53:3 (2013), 273–283  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    24. V. F. Butuzov, N. T. Levashova, A. A. Mel'nikova, “A steplike contrast structure in a singularly perturbed system of elliptic equations”, Comput. Math. Math. Phys., 53:9 (2013), 1239–1259  mathnet  crossref  crossref  isi  elib  elib
    25. E. A. Antipov, N. T. Levashova, N. N. Nefedov, “Asymptotics of the front motion in the reaction-diffusion-advection problem”, Comput. Math. Math. Phys., 54:10 (2014), 1536–1549  mathnet  crossref  crossref  elib
    26. N. N. Nefedov, E. I. Nikulin, “Existence and stability of periodic solutions for reaction-diffusion equations in the two-dimensional case”, Model. i analiz inform. sistem, 23:3 (2016), 342–348  mathnet  crossref  mathscinet  elib
    27. E. A. Antipov, V. T. Volkov, N. T. Levashova, N. N. Nefedov, “Reshenie vida dvizhuschegosya fronta dvumernoi zadachi reaktsiya-diffuziya”, Model. i analiz inform. sistem, 24:3 (2017), 259–279  mathnet  crossref  elib
    28. M. A. Davydova, S. A. Zakharova, N. T. Levashova, “On one model problem for the reaction-diffusion-advection equation”, Comput. Math. Math. Phys., 57:9 (2017), 1528–1539  mathnet  crossref  crossref  isi  elib  elib
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