Fermi-Dirac-Fokker-Planck equation: well-posedness and long-time asymptotics

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dc.creatorCarrillo, José A.
dc.creatorLaurençot, Philippe
dc.creatorRosado, Jesús
dc.date2008-01-18
dc.date.accessioned2026-07-07T08:55:20Z
dc.date.available2026-07-07T08:55:20Z
dc.descriptionA 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 asymptotics in $L^1$ are characterized by the Fermi-Dirac equilibrium with the same initial mass. This result is achieved without rate for any constructed global solution and with exponential rate due to entropy/entropy-dissipation arguments for initial data controlled by Fermi-Dirac distributions. Finally, initial data below radial solutions with suitable decay at infinity lead to solutions for which the relative entropy towards the Fermi-Dirac equilibrium is shown to converge to zero without decay rate.
dc.identifierhttps://arxiv.org/abs/0801.2888
dc.identifierhttp://arxiv.org/abs/0801.2888
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/146239
dc.subjectAnalysis of PDEs
dc.subject35B40; 35K15; 37B25
dc.titleFermi-Dirac-Fokker-Planck equation: well-posedness and long-time asymptotics
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