数学物理学报(英文版) ›› 2009, Vol. 29 ›› Issue (3): 552-568.doi: 10.1016/S0252-9602(09)60053-9

• 论文 • 上一篇    下一篇

THE WELL-POSEDNESS AND ASYMPTOTICS OF MULTI-DIMENSIONAL QUANTUM HYDRODYNAMICS

Hsiao Ling,Li Hailiang   

  1. Institute of Mathematics, AMSS,  |Chinese Academy of Sciences, Beijing 100190, China|Department of |Mathematics,   |Capital Normal University, Beijing 100037, China
  • 收稿日期:2008-10-15 出版日期:2009-05-20 发布日期:2009-05-20
  • 基金资助:

    L.H. is supported in part by the NSFC (10431060);  H.L. is supported partially by the NSFC (10431060,  10871134), the Beijing Nova program (2005B48), the NCET support of the Ministry of Education of China, and the Huo Ying Dong Foundation (111033)

THE WELL-POSEDNESS AND ASYMPTOTICS OF MULTI-DIMENSIONAL QUANTUM HYDRODYNAMICS

Hsiao Ling,Li Hailiang   

  • Received:2008-10-15 Online:2009-05-20 Published:2009-05-20
  • Supported by:

    L.H. is supported in part by the NSFC (10431060);  H.L. is supported partially by the NSFC (10431060,  10871134), the Beijing Nova program (2005B48), the NCET support of the Ministry of Education of China, and the Huo Ying Dong Foundation (111033)

摘要:

The multi-dimensional quantum hydrodynamic equations for charge transport in ultra-small electronic devices like semiconductors, where quantum effects (like particle tunnelling through potential barriers and built-up in quantum wells) take place, is considered in the present paper, and the recent progress on well-posedness, stability analysis, and small scaling limits are reviewed.

关键词: quantum hydrodynamics, well-posedness, longtime behavior, small scale limit

Abstract:

The multi-dimensional quantum hydrodynamic equations for charge transport in ultra-small electronic devices like semiconductors, where quantum effects (like particle tunnelling through potential barriers and built-up in quantum wells) take place, is considered in the present paper, and the recent progress on well-posedness, stability analysis, and small scaling limits are reviewed.

Key words: quantum hydrodynamics, well-posedness, longtime behavior, small scale limit

中图分类号: 

  • 35A07