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Comptes Rendus Mathématique
Volume 339, n° 10
pages 683-688 (novembre 2004)
Doi : 10.1016/j.crma.2004.09.025
Received : 6 May 2004 ;  accepted : 27 September 2004
A note on the long time behavior for the drift-diffusion-Poisson system
Une note sur le comportement en temps long du système dérive-diffusion-Poisson.
 

Naoufel Ben Abdallah , Florian Méhats , Nicolas Vauchelet
Mathématiques pour lʼindustrie et la physique, UMR 5640, université Paul Sabatier, UFR MIG, 118, route de Narbonne, 31032 Toulouse cedex 4, France 

Abstract

In this note we analyze the long time behavior of a drift-diffusion-Poisson system with a symmetric definite positive diffusion matrix, subject to Dirichlet boundary conditions. This system models the transport of electrons in semiconductor or plasma devices. By using a quadratic relative entropy obtained by keeping the lowest order term of the logarithmic relative entropy, we prove the exponential convergence to the equilibrium. To cite this article: N. Ben Abdallah et al., C. R. Acad. Sci. Paris, Ser. I 339 (2004).

The full text of this article is available in PDF format.
Résumé

Dans cette note, nous analysons le comportement en temps long des solutions du système couplé dérive-diffusion-Poisson avec une matrice de diffusion définie positive et soumis à des conditions aux limites de Dirichlet. Ce système modélise le transport de charges dans des dispositifs à semiconducteurs ou à plasmas. En utilisant lʼentropie relative développée à lʼordre 2, nous prouvons la convergence exponentielle des solutions vers lʼéquilibre. Pour citer cet article : N. Ben Abdallah et al., C. R. Acad. Sci. Paris, Ser. I 339 (2004).

The full text of this article is available in PDF format.

* Support by the European network HYKE, funded by the EC as contract HPRN-CT-2002-00282, is acknowledged.



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