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Mat. Sb., 2016, Volume 207, Number 8, Pages 73–100 (Mi msb8602)  

This article is cited in 3 scientific papers (total in 3 papers)

Asymptotic behaviour of the solution to a singularly perturbed partially dissipative system with a multiple root of the degenerate equation

V. F. Butuzov

Lomonosov Moscow State University, Faculty of Physics

Abstract: Asymptotic formulae for the solution of the initial-boundary value problem for a singularly perturbed partially dissipative system of reaction-diffusion type are constructed and justified. The system consists of a parabolic and an ordinary differential equation in the case when the corresponding degenerate equation has a root of multiplicity two. The behaviour of the boundary layer functions and the algorithm for constructing them are significantly distinct from the case of a simple (multiplicity-one) root of the degenerate equation.
Bibliography: 8 titles.

Keywords: singularly perturbed problem with a multiple root of the degenerate equation, boundary layer, partially dissipative system.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-04619-a
This research was carried out with the support of the Russian Foundation for Basic Research (grant no. 15-01-04619-a).


DOI: https://doi.org/10.4213/sm8602

Full text: PDF file (585 kB)
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English version:
Sbornik: Mathematics, 2016, 207:8, 1100–1126

Bibliographic databases:

UDC: 517.925.8
MSC: Primary 34E10; Secondary 35K57
Received: 24.09.2015 and 02.02.2016

Citation: V. F. Butuzov, “Asymptotic behaviour of the solution to a singularly perturbed partially dissipative system with a multiple root of the degenerate equation”, Mat. Sb., 207:8 (2016), 73–100; Sb. Math., 207:8 (2016), 1100–1126

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/msb/v207/i8/p73

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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. V. F. Butuzov, “Asymptotic behaviour of a boundary layer solution to a stationary partly dissipative system with a multiple root of the degenerate equation”, Sb. Math., 210:11 (2019), 1581–1608  mathnet  crossref  crossref  adsnasa  isi
    2. Butuzov V.F., “Asymptotics of a Spike Type Contrast Structure in a Problem With a Multiple Root of the Degenerate Equation”, Differ. Equ., 55:6 (2019), 758–775  crossref  mathscinet  zmath  isi
    3. Butuzov V.F., Nefedov N.N., Omel'chenko O.E., Recke L., Vii International Conference Problems of Mathematical Physics and Mathematical Modelling, Journal of Physics Conference Series, 1205, IOP Publishing Ltd, 2019  crossref  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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