Homogenization and Hydrodynamic Limit for Fermi‐Dirac Statistics Coupled to a Poisson Equation |
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Authors: | Nader Masmoudi Mohamed Lazhar Tayeb |
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Institution: | 1. Courant Institute, New York, NY, USA;2. Department of Mathematics, University of Tunis El‐Manar Faculty of Sciences of Tunis, El‐Manar, Tunisia |
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Abstract: | This paper deals with the diffusion approximation of a Boltzmann‐Poisson system modeling Fermi‐Dirac statistics in the presence of an extra external oscillating electrostatic potential. Here we extend the analysis done in 19] to the case of a nonlinear collision operator. In addition to the averaging lemma and control from entropy dissipation used in 19], here we use two‐scale Young measures and renormalization techniques to prove the convergence. This result rigorously justifies the formal analysis of 3]. © 2015 Wiley Periodicals, Inc. |
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