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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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_0362546X_v137_n_p291_Canizo |
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todo:paper_0362546X_v137_n_p291_Canizo2023-10-03T15:27:10Z The Fokker-Planck equation for bosons in 2D: Well-posedness and asymptotic behavior Cañizo, J.A. Carrillo, J.A. Laurençot, P. Rosado, J. Bose-Einstein Entropy method Long-time asymptotics Bosons Linear transformations Mathematical transformations Statistical mechanics Timing jitter Asymptotic behaviors Bose-Einstein Convergence to equilibrium Entropy functional Entropy methods Hopf-cole transformations Long-time asymptotics Radially symmetric solution Fokker Planck equation 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_0362546X_v137_n_p291_Canizo |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
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R-134 |
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Bose-Einstein Entropy method Long-time asymptotics Bosons Linear transformations Mathematical transformations Statistical mechanics Timing jitter Asymptotic behaviors Bose-Einstein Convergence to equilibrium Entropy functional Entropy methods Hopf-cole transformations Long-time asymptotics Radially symmetric solution Fokker Planck equation |
| spellingShingle |
Bose-Einstein Entropy method Long-time asymptotics Bosons Linear transformations Mathematical transformations Statistical mechanics Timing jitter Asymptotic behaviors Bose-Einstein Convergence to equilibrium Entropy functional Entropy methods Hopf-cole transformations Long-time asymptotics Radially symmetric solution Fokker Planck equation Cañizo, J.A. Carrillo, J.A. Laurençot, P. Rosado, J. The Fokker-Planck equation for bosons in 2D: Well-posedness and asymptotic behavior |
| topic_facet |
Bose-Einstein Entropy method Long-time asymptotics Bosons Linear transformations Mathematical transformations Statistical mechanics Timing jitter Asymptotic behaviors Bose-Einstein Convergence to equilibrium Entropy functional Entropy methods Hopf-cole transformations Long-time asymptotics Radially symmetric solution Fokker Planck equation |
| description |
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. |
| format |
JOUR |
| author |
Cañizo, J.A. Carrillo, J.A. Laurençot, P. Rosado, J. |
| author_facet |
Cañizo, J.A. Carrillo, J.A. Laurençot, P. Rosado, J. |
| author_sort |
Cañizo, J.A. |
| title |
The Fokker-Planck equation for bosons in 2D: Well-posedness and asymptotic behavior |
| title_short |
The Fokker-Planck equation for bosons in 2D: Well-posedness and asymptotic behavior |
| title_full |
The Fokker-Planck equation for bosons in 2D: Well-posedness and asymptotic behavior |
| title_fullStr |
The Fokker-Planck equation for bosons in 2D: Well-posedness and asymptotic behavior |
| title_full_unstemmed |
The Fokker-Planck equation for bosons in 2D: Well-posedness and asymptotic behavior |
| title_sort |
fokker-planck equation for bosons in 2d: well-posedness and asymptotic behavior |
| url |
http://hdl.handle.net/20.500.12110/paper_0362546X_v137_n_p291_Canizo |
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