The Fokker–Planck equation for bosons in 2D: Well-posedness and asymptotic behavior
| Autor: | José A. Cañizo, Jesús Rosado, Philippe Laurençot, José A. Carrillo |
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| Přispěvatelé: | The Royal Society, Engineering & Physical Science Research Council (E |
| Rok vydání: | 2016 |
| Předmět: |
DYNAMICS
MODELS Mathematics Applied LIMIT 01 natural sciences 0101 Pure Mathematics law.invention law 0102 Applied Mathematics Master equation GRAZING COLLISIONS Long-time asymptotics PARTICLES Entropy method BOLTZMANN-EQUATION 0101 mathematics Boson Physics Science & Technology Applied Mathematics 010102 general mathematics Mathematical analysis Fermion Bose-Einstein Boltzmann equation MASTER EQUATION Exponential function FERMIONS 010101 applied mathematics DERIVATION KINETIC-EQUATION Physical Sciences Fokker–Planck equation Mathematics Analysis Bose–Einstein condensate Well posedness |
| Zdroj: | Nonlinear Analysis. 137:291-305 |
| ISSN: | 0362-546X |
| DOI: | 10.1016/j.na.2015.07.030 |
| Popis: | We show that solutions of the 2D Fokker–Planck equation for bosons are defined globally in time and converge to equilibrium, and this convergence is shown to be exponential for radially symmetric solutions. The main observation is that a variant of the Hopf–Cole transformation relates the 2D equation in radial coordinates to the usual linear Fokker–Planck equation. Hence, radially symmetric solutions can be computed analytically, and our results for general (non radially symmetric) solutions follow from comparison and entropy arguments. In order to show convergence to equilibrium we also prove a version of the Csiszar–Kullback inequality for the Bose–Einstein–Fokker–Planck entropy functional. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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