Abstract
This paper is devoted to the rigorous derivation of the macroscopic limit of a Vlasov- Fokker-Planck equation in which the Laplacian is replaced by a fractional Laplacian. The evolution of the density is governed by a fractional heat equation with the addition of a convective term coming from the external force. The analysis is performed by a modified test function method and by obtaining a priori estimates from quadratic entropy bounds. In addition, we give the proof of existence and uniqueness of solutions to the fractional Vlasov-Fokker-Planck equation.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 469-488 |
| Number of pages | 20 |
| Journal | SIAM Journal on Mathematical Analysis |
| Volume | 51 |
| Issue number | 1 |
| DOIs | |
| State | Published - 2019 |
| Externally published | Yes |
Keywords
- Anomalous diffusion limit
- Fractional fokker-planck operator
- Fractional laplacian
- Kinetic equations
- Superdiffusion
ASJC Scopus subject areas
- Analysis
- Computational Mathematics
- Applied Mathematics
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