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Mat. Sb., 2001, Volume 192, Number 5, Pages 13–52 (Mi msb563)  

This article is cited in 10 scientific papers (total in 10 papers)

Global influence domains of stable solutions with internal layers

V. F. Butuzov, I. V. Nedelko

M. V. Lomonosov Moscow State University

Abstract: The initial-boundary-value problem is considered for a non-stationary equation of reaction-diffusion type with non-linearity having two stable zeros. The conditions imposed ensure the existence of a stable stationary solution with internal transition layer (a stable step-like contrast structure). The question of which initial functions belong to the influence domain of such a solution is studied.

DOI: https://doi.org/10.4213/sm563

Full text: PDF file (436 kB)
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English version:
Sbornik: Mathematics, 2001, 192:5, 651–691

Bibliographic databases:

UDC: 517.956.226
MSC: 35B40, 35K57
Received: 19.01.2000

Citation: V. F. Butuzov, I. V. Nedelko, “Global influence domains of stable solutions with internal layers”, Mat. Sb., 192:5 (2001), 13–52; Sb. Math., 192:5 (2001), 651–691

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. Butuzov V.F., Nedel'ko I.V., “On the formation of a steplike contrast structure in a parabolic system with different powers of a small parameter”, Dokl. Math., 67:3 (2003), 311–314  mathnet  mathscinet  mathscinet  zmath  isi  elib
    2. A. A. Plotnicov, “Modeling and numerical-analytic computations of contrast structures of variable type”, Comput. Math. Math. Phys., 43:2 (2003), 203–216  mathnet  mathscinet  zmath
    3. M. G. Dmitriev, G. S. Zhukova, A. P. Petrov, “Asimptoticheskii analiz modeli “vlast-obschestvo” dlya sluchaya dvukh ustoichivykh raspredelenii vlasti”, Matem. modelirovanie, 16:5 (2004), 23–34  mathnet  mathscinet
    4. Butuzov V.F., Nedel'ko I.V., “On the formation of a solution with an internal layer in a parabolic system with different powers of a small parameter”, Differ. Equ., 40:3 (2004), 382–395  mathnet  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    5. V. F. Butuzov, S. A. Kryazhimskii, I. V. Nedelko, “Global domain of attraction of a step-like contrast structure in a critical case”, Comput. Math. Math. Phys., 44:8 (2004), 1334–1355  mathnet  mathscinet  zmath  elib
    6. A. A. Plotnicov, “Stability of the simplest boundary layer solutions and of the contrast structures”, Comput. Math. Math. Phys., 44:8 (2004), 1356–1365  mathnet  mathscinet  zmath  elib
    7. V. F. Butuzov, S. A. Kryazhimskii, I. V. Nedelko, “On the global domain of influence of stable steplike contrast structures in the Dirichlet problem”, Comput. Math. Math. Phys., 44:6 (2004), 985–1006  mathnet  mathscinet  zmath
    8. V. T. Volkov, N. E. Grachëv, N. N. Nefedov, A. N. Nikolaev, “On the formation of sharp transition layers in two-dimensional reaction-diffusion models”, Comput. Math. Math. Phys., 47:8 (2007), 1301–1309  mathnet  crossref  mathscinet  elib
    9. Omel'chenko O., Recke L., “Boundary layer solutions to singularly perturbed problems via the implicit function theorem”, Asymptot. Anal., 62:3-4 (2009), 207–225  mathscinet  zmath  isi  elib
    10. M. G. Dmitriev, A. A. Pavlov, A. P. Petrov, “Nonstationary Fronts in the Singularly Perturbed Power-Society Model”, Abstract and Applied Analysis, 2013 (2013), 1  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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