一维单极粘滞量子流体力学稳态模型的解  

The Steady-state Solutions to The Unipolar Viscous Quantum Hydrodynamic Model in One Space Dimension

作　　者：毛磊[1] 王锋[2] 张纯[1] 寇冰煜[1] 

机构地区：[1]中国人民解放军理工大学理学院,211101 [2]苏宁环球集团,江苏省南京市210098

出　　处：《曲阜师范大学学报（自然科学版）》2010年第3期51-56,119,共7页Journal of Qufu Normal University(Natural Science)

摘　　要：研究了一类一维稳态单极半导体方程的粘滞量子流体力学模型.这类模型比较复杂,以往的数学著作中讨论的不多.文章在同一模型中将等温和等熵两种情形一起讨论.在有界区间(0,1)中假设压力函数只与粒子浓度有关,通过边界条件先将原方程组变形为常见的形式,得到原问题的等价问题.再做先验估计,利用隐函数定理、Leray-Schauder不动点定理等证明等价问题的解存在且惟一,从而证明了原单极粘滞量子流体力学模型存在惟一稳态解.The steady-state unipolar viscous quantum hydrodynamic model in one space dimension is studied.For the viscous quantum hydrodynamic model is difficult to be dealed with,there are only a few works had discussed on it.Isothermal model and the isentropic model have been discussed in the article simultaneously.The problem is considered on a bounded interval（0,1） with the pressure function only determined by particles density.We simplified the model to a common one under the assumption of the boundary conditions.By a priori estimates,using the implicit function theorem,Leray-Schauder fixed point theorem is equivalent to issues such as proof of the existence and unique solution,which proves the original unipolar existence and uniqueness of viscous quantum hydrodynamic model for steady-state solution.

关 键 词：粘滞量子流体力学 稳态 单极 存在性 惟一性 隐函数定理 不动点定理 

分 类 号：O175.15[理学—数学]