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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2019, Volume 59, Number 9, Pages 1581–1590
DOI: https://doi.org/10.1134/S0044466919090072
(Mi zvmmf10956)
 

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

Corner boundary layer in boundary value problems for singularly perturbed parabolic equations with nonmonotonic nonlinearities

I. V. Denisova, A. I. Denisovb

a Tula State Lev Tolstoy Pedagogical University, Tula, 300026 Russia
b National Research University Higher School of Economics, Moscow, 101000 Russia
Citations (5)
References:
Abstract: For a singularly perturbed parabolic equation ${{\epsilon }^{2}}\left( {{{a}^{2}}\frac{{{{\partial }^{2}}u}}{{\partial {{x}^{2}}}} - \frac{{\partial u}}{{\partial t}}} \right) = F(u,x,t,\epsilon )$ in a rectangle, a problem with boundary conditions of the first kind is considered. At the corner points of the rectangle, the function $F$ is assumed to be quadratic and nonmonotonic with respect to the variable $u$ on the interval from the root of the degenerate equation to the boundary value. The main attention is paid to constructing the main term of the corner part of the asymptotics of the solution as $\epsilon\to0$ .
Key words: boundary layer, asymptotic approximation, singularly perturbed equation.
Received: 02.04.2019
Revised: 02.04.2019
Accepted: 15.05.2019
English version:
Computational Mathematics and Mathematical Physics, 2019, Volume 59, Issue 9, Pages 1518–1527
DOI: https://doi.org/10.1134/S0965542519090070
Bibliographic databases:
Document Type: Article
UDC: 517.956.4
Language: Russian
Citation: I. V. Denisov, A. I. Denisov, “Corner boundary layer in boundary value problems for singularly perturbed parabolic equations with nonmonotonic nonlinearities”, Zh. Vychisl. Mat. Mat. Fiz., 59:9 (2019), 1581–1590; Comput. Math. Math. Phys., 59:9 (2019), 1518–1527
Citation in format AMSBIB
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  • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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