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Zh. Vychisl. Mat. Mat. Fiz., 2019, Volume 59, Number 1, Pages 102–117 (Mi zvmmf10820)  

This article is cited in 1 scientific paper (total in 1 paper)

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

A. I. Denisova, I. V. Denisovb

a National Research University Higher School of Economics, Moscow, 101000 Russia
b Tula State Lev Tolstoy Pedagogical University, Tula, 300026 Russia

Abstract: A singularly perturbed parabolic equation ${{\varepsilon }^{2}}( {{{a}^{2}}\frac{{{{\partial }^{2}}u}}{{\partial {{x}^{2}}}} - \frac{{\partial u}}{{\partial t}}} ) = F(u,x,t,\varepsilon )$ is considered in a rectangle with the boundary conditions of the first kind. At the corner points of the rectangle, the monotonicity of the function $F$ with respect to the variable $u$ in the interval from the root of the degenerate equation to the boundary value is not required. The asymptotic approximation of the solution is constructed under the assumption that the principal term of the corner part exists. A complete asymptotic expansion of the solution as $\varepsilon\to 0$ is constructed, and its uniformity in a closed rectangle is proved.

Key words: boundary layer, asymptotic approximation, singularly perturbed equation.

DOI: https://doi.org/10.1134/S004446691901006X


English version:
Computational Mathematics and Mathematical Physics, 2019, 59:1, 96–111

Bibliographic databases:

UDC: 519.634
Received: 05.02.2018

Citation: A. I. Denisov, I. V. Denisov, “Corner boundary layer in boundary value problems for singularly perturbed parabolic equations with nonlinearities”, Zh. Vychisl. Mat. Mat. Fiz., 59:1 (2019), 102–117; Comput. Math. Math. Phys., 59:1 (2019), 96–111

Citation in format AMSBIB
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\paper Corner boundary layer in boundary value problems for singularly perturbed parabolic equations with nonlinearities
\jour Zh. Vychisl. Mat. Mat. Fiz.
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\pages 102--117
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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. I. V. Denisov, A. I. Denisov, “Matematicheskie modeli protsessov goreniya”, MaterialyVserossiiskoinauchnoikonferentsii Differentsialnye uravneniyai ikh prilozheniya,posvyaschennoi 85-letiyu professoraM.T.Terekhina.Ryazanskii gosudarstvennyi universitet im. S.A. Esenina,Ryazan, 1718 maya2019 g. Chast 1, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 185, VINITI RAN, M., 2020, 50–57  mathnet  crossref
  •      Computational Mathematics and Mathematical Physics
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