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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2024. Vol 48

Convergence of Approximate Solutions for Transport-diffusion Equation in the Half-space with Neumann Condition

Author(s)
Rabah Gherdaoui1, Steave Selvaduray2, Hisao Fujita Yashima3

1Universit´e de Tizi Ouzou, Tizi Ouzou, Algeria

2Universit`a di Torino, Turin, Italy

3Ecole Normale Sup´erieure de Constantine, Constantine, Algeria

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.
About the Authors

Rabah Gherdaoui, PhD, Universit´e de Tizi Ouzou, Tizi Ouzou, 15000, Algeria, rabah.gherdaoui@ummto.dz

Steave Selvaduray, PhD, Universit`a di Torino, Turin, 10124, Italy, steave selva@yahoo.it

Hisao Fujita Yashima, Prof., Ecole ´ Normale Sup´erieure de Constantine, Constantine, 25000, Algeria, hisaofujitayashima@yahoo.com

For citation

Gherdaoui R., Selvaduray S., Fujita Yashima H. Convergence of Approximate Solutions for Transport-diffusion Equation in the Half-space with Neumann Condition. The Bulletin of Irkutsk State University. Series Mathematics, 2024, vol. 48, pp. 64–79. (in Russian)

https://doi.org/10.26516/1997-7670.2024.48.64

Keywords
transport-diffusion equation, homogenous Neumann condition, approximate solution, heat kernel
UDC
517.956.4
MSC
35K58, 35K15
DOI
https://doi.org/10.26516/1997-7670.2024.48.64
References
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