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

Christian Dogbe

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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 d\'{e}duisons et analysons le mod\`{e}le Spherical Harmonics Expansion (SHE) gen\'{e}ralisant le modele de D\'{e}rive Diffusion (DD) en ce qu'il d\'{e}crit le comportement d'un nuage de particules en fonction du temps, de la position et d'une variable d''energie (alors que les mod\`{e}les du type DD ne prennent pas en compte l''energie des particules. Nous prouvons galement que le comportement diffusif se produit sur de longues \'{e}chelles de temps et de distance et nous d\'{e}terminons le tenseur de diffusion. L'analyse est bas\'{e}e sur les \'{e}quations cin\'{e}tiques intervenant dans le transport d'\'{e}lectron 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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