Abstract
We study the diffusion limit of the Vlasov-Poisson-Fokker-Planck System. Here, we generalize the local in time results and the two dimensional results of Poupaud-Soler [F. Poupaud and J. Soler, Math. Models Methods Appl. Sci., 10(7), 1027-1045, 2000] and Goudon [T. Goudon, Math. Models Methods Appl. Sci., 15(5), 737-752, 2005] to the case of several space dimensions. Renormalization techniques, the method of moments and a velocity averaging lemma are used to prove the convergence of free energy solutions (renormalized solutions) to the Vlasov-Poisson-Fokker-Planck system towards a global weak solution of the Drift-Diffusion-Poisson model.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 463-479 |
| Number of pages | 17 |
| Journal | Communications in Mathematical Sciences |
| Volume | 8 |
| Issue number | 2 |
| DOIs | |
| State | Published - Jun 2010 |
Keywords
- Drift-Diffusion-Poisson model
- Hydrodynamic limit
- Moment method
- Renormalized solutions
- Velocity averaging lemma
- Vlasov-Poisson-Fokker-Planck system
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics