Geodesic
Convergence of approximate solutions for transport-diffusion equation in the half-space with Neumann condition
The Bulletin of Irkutsk State University. Series Mathematics, Tome 48 (2024), pp. 64-79

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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.
Mots-clés : transport-diffusion equation
Keywords: homogenous Neumann condition, approximate solution, heat kernel. 
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     author = {Rabah Gherdaoui and Steave Selvaduray and Hisao Fujita Yashima},
     title = {Convergence of approximate solutions for transport-diffusion equation in the half-space with {Neumann} condition},
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     pages = {64--79},
     publisher = {mathdoc},
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     url = {http://geodesic.mathdoc.fr/item/IIGUM_2024_48_a4/}
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Rabah Gherdaoui; Steave Selvaduray; Hisao Fujita Yashima. Convergence of approximate solutions for transport-diffusion equation in the half-space with Neumann condition. The Bulletin of Irkutsk State University. Series Mathematics, Tome 48 (2024), pp. 64-79. http://geodesic.mathdoc.fr/item/IIGUM_2024_48_a4/