Ja n 20 08 Fermi-Dirac-Fokker-Planck Equation : Well-posedness & Long-time Asymptotics

@inproceedings{Carrillo2008JaN2,
  title={Ja n 20 08 Fermi-Dirac-Fokker-Planck Equation : Well-posedness & Long-time Asymptotics},
  author={Jos{\'e} A. Carrillo and Philippe Laurençot and Jes{\'u}s Rosado},
  year={2008}
}
A Fokker-Planck type equation for interacting particles with exclusion principle is analysed. The nonlinear drift gives rise to mathematical difficulties in controlling moments of the distribution function. Assuming enough initial moments are finite, we can show the global existence of weak solutions for this problem. The natural associated entropy of the equation is the main tool to derive uniform in time a priori estimates for the kinetic energy and entropy. As a consequence, long-time… CONTINUE READING

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