Abstract
An approximation by diffusion of a nonlinear Boltzmann equation modeling a Fermi-Dirac statistics is analyzed for an unbounded velocity space and Poisson coupling. A careful analysis of the entropy and entropy-dissipation allows to control the distribution function and to pass to the limit using duality method.
Original language | English (US) |
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Pages (from-to) | 42-70 |
Number of pages | 29 |
Journal | Journal des Mathematiques Pures et Appliquees |
Volume | 158 |
DOIs | |
State | Published - Feb 2022 |
Keywords
- Boltzmann-Poisson
- Entropy-dissipation
- Fermi-Dirac statistics
- Hydrodynamic limit
- Quantum effects
- Semiconductors
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics