数学物理学报(英文版) ›› 2015, Vol. 35 ›› Issue (1): 140-156.doi: 10.1016/S0252-9602(14)60147-8

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GLOBAL CLASSICAL SOLUTIONS FOR QUANTUM KINETIC FOKKER-PLANCK EQUATIONS

罗兰|张新平   

  1. School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China|Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes, Guangzhou University, Guangzhou 510006, China Department of Mathematics and Sciences, Luoyang Institute of Science and Technology, Luoyang 471023, China
  • 收稿日期:2013-12-13 修回日期:2014-03-10 出版日期:2015-01-20 发布日期:2015-01-20
  • 基金资助:

    This research was supported by the National Natural Science Foundation of China (11371151).

GLOBAL CLASSICAL SOLUTIONS FOR QUANTUM KINETIC FOKKER-PLANCK EQUATIONS

LUO Lan, ZHANG XinPing   

  1. School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China|Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes, Guangzhou University, Guangzhou 510006, China Department of Mathematics and Sciences, Luoyang Institute of Science and Technology, Luoyang 471023, China
  • Received:2013-12-13 Revised:2014-03-10 Online:2015-01-20 Published:2015-01-20
  • Supported by:

    This research was supported by the National Natural Science Foundation of China (11371151).

摘要:

We consider a class of nonlinear kinetic Fokker-Planck equations modeling quantum particles which obey the Bose-Einstein and Fermi-Dirac statistics, respectively. We establish the existence and convergence rate to the steady state of global classical solution to such kind of equations around the steady state.

关键词: quantum Fokker-Planck equations, energy method, convergence rates

Abstract:

We consider a class of nonlinear kinetic Fokker-Planck equations modeling quantum particles which obey the Bose-Einstein and Fermi-Dirac statistics, respectively. We establish the existence and convergence rate to the steady state of global classical solution to such kind of equations around the steady state.

Key words: quantum Fokker-Planck equations, energy method, convergence rates

中图分类号: 

  • 35Q99