Annales Mathématiques Africaines


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Convergence de la Solution d’une équation de Transport-diffusion vers la Solution d’une équation de Transport



Latifa Ait MAHIOUT(1) et Hisao Fujita Yashima(2)
École Normale Supérieure de Constantine, Algérie.



Mathematics Subject Classification: (2010) 35K15, 35K58, 35L03, 35Q49
Key words: Transport-diffusion equation, transport equation, vanishing diffusion coefficient, approximate solutions




Abstract:

Transport equation and transport-diffusion equation obtained by adding a diffusion term κΔu are considered in d. For transport-diffusion equation, we consider a family of approximate solutions which are defined by the application of the integral operator corresponding to the fundamental solution of the heat equation on each step of discretized time. For transport equation also we consider a family of approximate solutions defined on the same family of time discretizations. By using the estimate of the difference between approximate solution for transport-diffusion equation and that for transport equation, we prove the convergence of the solution of transport-diffusion equation to that of transport equation when κ tends to 0. This result also asserts that the difference between each term in the transport-diffusion equation and the corresponding term in the transport equation is bounded proportionally to κ.

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