Abstract:
In this paper, we examine the question about the approximation of the solution to a transport-diffusion equation in a half-space with the homogenous Neumann condition. Using heat kernel and translation corresponding to the transport in each step of time discretization, we construct a family of approximate solutions. By even extension the given functions and the approximate solutions are transformed into functions defined on the whole space, what makes it possible to establish estimates of approximate solutions and their derivatives and to prove their convergence. We show that the limit function satisfies the equation and the boundary condition.
Citation:
Rabah Gherdaoui, Steave Selvaduray, Hisao Fujita Yashima, “Convergence of approximate solutions for transport-diffusion equation in the half-space with Neumann condition”, Bulletin of Irkutsk State University. Series Mathematics, 48 (2024), 64–79
\Bibitem{GheSelFuj24}
\by Rabah~Gherdaoui, Steave~Selvaduray, Hisao~Fujita~Yashima
\paper Convergence of approximate solutions for transport-diffusion equation in the half-space with Neumann condition
\jour Bulletin of Irkutsk State University. Series Mathematics
\yr 2024
\vol 48
\pages 64--79
\mathnet{http://mi.mathnet.ru/iigum565}
\crossref{https://doi.org/10.26516/1997-7670.2024.48.64}
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https://www.mathnet.ru/eng/iigum565
https://www.mathnet.ru/eng/iigum/v48/p64
This publication is cited in the following 2 articles:
Lynda Taleb, Rabah Gherdaoui, “Approximation by the heat kernel of the solution to the transport-diffusion equation with the time-dependent diffusion coefficient”, MATH, 10:2 (2025), 2392
A. Nemdili, F. Korishi, Kh. Fuzhita Yashima, “Priblizhenie resheniya uravneniya perenosa-diffuzii v prostranstve Geldera”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 28:3 (2024), 426–444
Citation in format AMSBIB
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