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Zh. Vychisl. Mat. Mat. Fiz., 2015, Volume 55, Number 1, Pages 22–33 (Mi zvmmf10132)  

This article is cited in 2 scientific papers (total in 2 papers)

Estimating the smoothness of the regular component of the solution to a one-dimensional singularly perturbed convection-diffusion equation

V. B. Andreev

Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119992, Russia

Abstract: The first boundary value problem for a one-dimensional singularly perturbed convection-diffusion equation with variable coefficients on a finite interval is considered. For the regular component of the solution, unimprovable a priori estimates in the Hölder norms are obtained. The estimates are unimprovable in the sense that they fail on any weakening of the estimating norm.

Key words: singularly perturbed equation, convection-diffusion, decomposition of solution, unimprovable estimates, Hölder spaces.

DOI: https://doi.org/10.7868/S0044466915010032

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English version:
Computational Mathematics and Mathematical Physics, 2015, 55:1, 19–30

Bibliographic databases:

UDC: 519.624.2
Received: 26.05.2014

Citation: V. B. Andreev, “Estimating the smoothness of the regular component of the solution to a one-dimensional singularly perturbed convection-diffusion equation”, Zh. Vychisl. Mat. Mat. Fiz., 55:1 (2015), 22–33; Comput. Math. Math. Phys., 55:1 (2015), 19–30

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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. E. O'Riordan, “Interior layers in singularly perturbed problems”, Differential Equations and Numerical Analysis, Springer Proceedings in Mathematics & Statistics, 172, eds. V. Sigamani, J. Miller, R. Narasimhan, P. Mathiazhagan, F. Victor, Springer India, 2016, 25–40  crossref  mathscinet  zmath  isi
    2. V. B. Andreev, “Hölder estimates for the regular component of the solution to a singularly perturbed convection-diffusion equation”, Comput. Math. Math. Phys., 57:12 (2017), 1935–1972  mathnet  crossref  crossref  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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