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  to the case of a nonlinear collision operator. In addition to the averaging lemma and control from entropy dissipation used in , here we use two-scale Young measures and renormalization techniques to prove the convergence. This result rigorously justifies the formal analysis of .
|Original language||English (US)|
|Number of pages||32|
|Journal||Communications on Pure and Applied Mathematics|
|State||Published - Oct 1 2015|
ASJC Scopus subject areas
- Applied Mathematics