A note on the long time behavior for the drift-diffusion-Poisson system |
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Authors: | Naoufel Ben Abdallah Florian Méhats Nicolas Vauchelet |
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Institution: | 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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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). |
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