Comptes Rendus
Partial Differential Equations
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.]
Comptes Rendus. Mathématique, Volume 339 (2004) no. 10, pp. 683-688.

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 l'entropie relative développée à l'ordre 2, nous prouvons la convergence exponentielle des solutions vers l'équilibre.

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.

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DOI : 10.1016/j.crma.2004.09.025

Naoufel Ben Abdallah 1 ; Florian Méhats 1 ; Nicolas Vauchelet 1

1 Mathématiques pour l'industrie et la physique, UMR 5640, université Paul Sabatier, UFR MIG, 118, route de Narbonne, 31032 Toulouse cedex 4, France
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Naoufel Ben Abdallah; Florian Méhats; Nicolas Vauchelet. A note on the long time behavior for the drift-diffusion-Poisson system. Comptes Rendus. Mathématique, Volume 339 (2004) no. 10, pp. 683-688. doi : 10.1016/j.crma.2004.09.025. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.09.025/

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

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