Convergence of Approximate Solutions for Transport-diffusion Equation in the Half-space with Neumann Condition
| Autor: | R. Gherdaoui, S. Selvaduray, H. Fujita Yashima |
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| Jazyk: | English<br />Russian |
| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | Известия Иркутского государственного университета: Серия "Математика", Vol 48, Iss 1, Pp 64-79 (2024) |
| Druh dokumentu: | article |
| ISSN: | 1997-7670 2541-8785 |
| DOI: | 10.26516/1997-7670.2024.48.64 |
| Popis: | 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. |
| Databáze: | Directory of Open Access Journals |
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