The Fokker-Planck equation for bosons in 2D: Well-posedness and asymptotic behavior

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 equatio...

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Detalles Bibliográficos
Autores principales: Cañizo, J.A., Carrillo, J.A., Laurençot, P., Rosado, J.
Formato: JOUR
Materias:
Bose-Einstein
Entropy method
Long-time asymptotics
Bosons
Linear transformations
Mathematical transformations
Statistical mechanics
Timing jitter
Asymptotic behaviors
Convergence to equilibrium
Entropy functional
Entropy methods
Hopf-cole transformations
Radially symmetric solution
Fokker Planck equation
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_0362546X_v137_n_p291_Canizo
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
Descripción
Sumario: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 Csiszár-Kullback inequality for the Bose-Einstein-Fokker-Planck entropy functional. © 2015 Elsevier Ltd. All rights reserved.

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