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Zh. Vychisl. Mat. Mat. Fiz., 2019, Volume 59, Number 2, Pages 264–276 (Mi zvmmf10834)  

Estimates in Hölder classes for the solution of an inhomogeneous Dirichlet problem for a singularly perturbed homogeneous convection-diffusion equation

V. B. Andreev, I. G. Beluhina

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

Abstract: An inhomogeneous Dirichlet boundary value problem for a singularly perturbed homogeneous convection-diffusion equation with constant coefficients is considered in a half-plane. Convection is assumed to be directed orthogonally to the half-plane boundary away from it. Assuming that the boundary function is from the space $C^{2,\lambda}$, $0<\lambda<1$, an unimprovable estimate for the solution bounded at infinity is obtained in the appropriate Hölder norm.

Key words: singularly perturbed equation, convectiondiffusion, problem in a half-plane, unimprovable a priori estimates, Hölder spaces.

DOI: https://doi.org/10.1134/S0044466919020030


English version:
Computational Mathematics and Mathematical Physics, 2019, 59:2, 253–265

Bibliographic databases:

UDC: 517.958
Received: 25.03.2018
Revised: 03.09.2018

Citation: V. B. Andreev, I. G. Beluhina, “Estimates in Hölder classes for the solution of an inhomogeneous Dirichlet problem for a singularly perturbed homogeneous convection-diffusion equation”, Zh. Vychisl. Mat. Mat. Fiz., 59:2 (2019), 264–276; Comput. Math. Math. Phys., 59:2 (2019), 253–265

Citation in format AMSBIB
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