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Spherical Harmonics Expansion of the Vlasov-Poisson initial bounary value problem

Christian Dogbe
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Abstract

We derive and analyze the ‘SHE' (Spherical Harmonics Expansion) type system of equations coupled in energy. We also show that diffusive behavior occurs on long time and distance scales and we determine the diffusion tensor. The analysis is based on the governing kinetic equations arising in electron transport in semiconductors ----- Nous déduisons et analysons le modèle Spherical Harmonics Expansion (SHE) genéralisant le modele de Dérive Diffusion (DD) en ce qu'il décrit le comportement d'un nuage de particules en fonction du temps, de la position et d'une variable d''energie (alors que les modèles du type DD ne prennent pas en compte l''energie des particules. Nous prouvons galement que le comportement diffusif se produit sur de longues échelles de temps et de distance et nous déterminons le tenseur de diffusion. L'analyse est basée sur les équations cinétiques intervenant dans le transport d'électron en semi-conducteurs.

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Christian Dogbe. 2005-11-04. Spherical Harmonics Expansion of the Vlasov-Poisson initial bounary value problem. https://arxiv.org/abs/math/0511103

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