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Zh. Vychisl. Mat. Mat. Fiz., 2012, Volume 52, Number 6, Pages 1042–1047 (Mi zvmmf9620)  

This article is cited in 4 scientific papers (total in 4 papers)

The initial boundary value problem for a nonlocal singularly perturbed reaction–diffusion equation

N. N. Nefedov, A. G. Nikitin

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

Abstract: The initial boundary value problem for a nonlinear singularly perturbed integro-parabolic equation is examined. An asymptotic expansion of the solution to this problem containing the temporal, spatial and corner boundary layers is constructed. The existence and local uniqueness of the solution is justified by using the asymptotic method of differential inequalities.

Key words: reaction–diffusion problem, singularly perturbed integro-parabolic equation, boundary layers, asymptotic expansion of solution

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English version:
Computational Mathematics and Mathematical Physics, 2012, 52:6, 926–931

Bibliographic databases:

UDC: 519.633
Received: 30.06.2011
Revised: 15.12.2011

Citation: N. N. Nefedov, A. G. Nikitin, “The initial boundary value problem for a nonlocal singularly perturbed reaction–diffusion equation”, Zh. Vychisl. Mat. Mat. Fiz., 52:6 (2012), 1042–1047; Comput. Math. Math. Phys., 52:6 (2012), 926–931

Citation in format AMSBIB
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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. A. Archibasov, A. Korobeinikov, V. A. Sobolev, “Asymptotic expansions of solutions in a singularly perturbed model of virus evolution”, Comput. Math. Math. Phys., 55:2 (2015), 240–250  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    2. O. P. Filatov, “Globalnaya teorema suschestvovaniya i edinstvennosti resheniya pervoi kraevoi zadachi dlya nelineinogo integrodifferentsialnogo uravneniya parabolicheskogo tipa”, Vestn. SamGU. Estestvennonauchn. ser., 2015, no. 3(125), 64–72  mathnet  elib
    3. Archibasov A.A., Korobeinikov A., Sobolev V.A., “Passage to the limit in a singularly perturbed partial integro-differential system”, Differ. Equ., 52:9 (2016), 1115–1122  crossref  mathscinet  zmath  isi  elib  scopus
    4. S. K. Zarifzoda, R. N. Odinaev, “Issledovanie nekotorykh klassov integro-differentsialnykh uravnenii v chastnykh proizvodnykh vtorogo poryadka so stepenno-logarifmicheskoi osobennostyu v yadre”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2020, no. 67, 40–54  mathnet  crossref
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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