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

作　　者：肖玲 李海梁 

机构地区：[1]Institute of Mathematics, AMSS, Chinese Academy of Sciences,Beijing 100190, China [2]Department of Mathematics, Capital Normal University,Beijing 100037, China

出　　处：《Acta Mathematica Scientia》2009年第3期552-568,共17页数学物理学报（B辑英文版）

基　　金：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.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 

分 类 号：O471.1[理学—半导体物理]