量子流体动力学等温模型的拟中性极限  

Quasineutral Limit of Isothermalk Quantum Hydrodynamic Model

作　　者：董建伟[1] 娄光谱[1] 

机构地区：[1]郑州航空工业管理学院数理系,河南郑州450015

出　　处：《中北大学学报（自然科学版）》2012年第2期102-106,共5页Journal of North University of China(Natural Science Edition)

基　　金：河南省高等学校青年骨干教师资助计划项目(2006110016);河南省教育厅科学技术研究重点项目(12A110024)

摘　　要：研究三维量子流体动力学等温模型,它是用来模拟超小半导体器件发生量子效应的宏观量子模型之一,反映了电子浓度、电子速度以及静电场位势之间的非线性关系.该模型中含有非线性三阶导数项,这在数学上给研究该模型带来了困难.在周期边界条件下。The isothermal quantum hydrodynamic model in three dimensional space is investigated.The model is one of the quantum macroscopic models used to simulate the quantum effects in miniaturized semiconductor devices,and it reflects the nonlinear relation among the electron density,the electron velocity and the electrostatic potential.The model contains a nonlinear third-order derivative item,which induces mathematical difficulties.By using the energy functional method and the weak convergence compactness method,the smooth solution of the model converges to the strong solution of incompressible Euler equations is proved under periodic boundary conditions.

关 键 词：量子流体动力学模型 周期边界条件 拟中性极限 

分 类 号：O175.29[理学—数学]