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Izv. RAN. Ser. Mat., 2002, Volume 66, Issue 1, Pages 3–42 (Mi izv369)  

This article is cited in 5 scientific papers (total in 5 papers)

On the global domain of influence of stable solutions with interior layers in the two-dimensional case

V. F. Butuzov, I. V. Nedelko

M. V. Lomonosov Moscow State University, Faculty of Physics

Abstract: We consider the initial-boundary problem for the singularly perturbed non-stationary reaction-diffusion equation with non-linearity of cubic type. We impose conditions sufficient for the existence of a stable stationary solution with an interior transition layer in the neighbourhood of a certain curve. We investigate the set of initial functions belonging to the domain of influence of this solution.

DOI: https://doi.org/10.4213/im369

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English version:
Izvestiya: Mathematics, 2002, 66:1, 1–40

Bibliographic databases:

UDC: 517.956.226
MSC: 35J60, 35B45, 35B20, 35B25, 35J65, 35B35, 35C20
Received: 20.03.2001

Citation: V. F. Butuzov, I. V. Nedelko, “On the global domain of influence of stable solutions with interior layers in the two-dimensional case”, Izv. RAN. Ser. Mat., 66:1 (2002), 3–42; Izv. Math., 66:1 (2002), 1–40

Citation in format AMSBIB
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\by V.~F.~Butuzov, I.~V.~Nedelko
\paper On the global domain of influence of stable solutions with interior layers in the two-dimensional case
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\pages 3--42
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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. A. B. Vasil'eva, E. E. Bukzhalev, “On the stability of a steplike contrast structure for a parabolic equation”, Comput. Math. Math. Phys., 45:3 (2005), 430–443  mathnet  mathscinet  zmath  elib  elib
    2. Nedel'ko I.V., “Onset of solutions with internal layers approaching the domain boundary”, Differ. Equ., 42:1 (2006), 112–125  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
    3. E. E. Bukzhalev, A. B. Vasil'eva, “Solutions to a singularly perturbed parabolic equation with internal and boundary layers depending on stretched variables of different orders”, Comput. Math. Math. Phys., 47:3 (2007), 407–419  mathnet  crossref  mathscinet  zmath  elib  elib
    4. Jia-qi Mo, Ming-kang Ni, “Recent progress in study of singular perturbation problems”, J of Shanghai Univ, 13:1 (2009), 1  crossref  mathscinet  zmath  isi  scopus
    5. 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
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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