Analysis of the viscous quantum hydrodynamic equations for semiconductors

被引:48
|
作者
Gualdini, MP [1 ]
Jüngel, A [1 ]
机构
[1] Univ Mainz, Fac Math & Informat, D-55099 Mainz, Germany
关键词
D O I
10.1017/S0956792504005686
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The steady-state viscous quantum hydrodynamic model in one space dimension is studied. The model consists of the continuity equations for the particle and current densities, coupled to the Poisson equation for the electrostatic potential. The equations are derived from a Wigner-Fokker-Planck model and they contain a third-order quantum correction term and second-order viscous terms. The existence of classical solutions is proved for "weakly supersonic" quantum flows. This means that a smallness condition on the particle velocity is still needed but the bound is allowed to be larger than for classical subsonic flows. Furthermore, the uniqueness of solutions and various asymptotic limits (semiclassical and inviscid limits) are investigated. The proofs are based on a reformulation of the problem as a fourth-order elliptic equation by using an exponential variable transformation.
引用
收藏
页码:577 / 595
页数:19
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