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Zh. Vychisl. Mat. Mat. Fiz., 2017, Volume 57, Number 12, Pages 1983–2020 (Mi zvmmf10650)  

Hölder estimates for the regular component of the solution to a singularly perturbed convection-diffusion equation

V. B. Andreev

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

Abstract: In a half-plane, a homogeneous Dirichlet boundary value problem for an inhomogeneous singularly perturbed convection-diffusion equation with constant coefficients and convection directed orthogonally away from the boundary of the half-plane is considered. Assuming that the right-hand side of the equation belongs to the space $C^\lambda$, $0<\lambda<1$, and the solution is bounded at infinity, an unimprovable estimate of the solution is obtained in a corresponding Hölder norm (anisotropic with respect to a small parameter).

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

DOI: https://doi.org/10.7868/S0044466917120055

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English version:
Computational Mathematics and Mathematical Physics, 2017, 57:12, 1935–1972

Bibliographic databases:

UDC: 519.63
Received: 03.03.2016

Citation: V. B. Andreev, “Hölder estimates for the regular component of the solution to a singularly perturbed convection-diffusion equation”, Zh. Vychisl. Mat. Mat. Fiz., 57:12 (2017), 1983–2020; Comput. Math. Math. Phys., 57:12 (2017), 1935–1972

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  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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