有界域上三维非等熵半导体方程解的渐近性(英文)  

ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR A 3D NONISENTROPIC HYDRODYNAMIC SEMICONDUCTOR MODEL IN A BOUNDED DOMAIN

作　　者：周芳[1] 

机构地区：[1]咸宁学院数学与统计学院,湖北咸宁437100

出　　处：《数学杂志》2012年第2期281-295,共15页Journal of Mathematics

基　　金：Supported by the National Science Foundation of China (11171223)

摘　　要：本文讨论了一类三维非等熵半导体方程. 利用能量估计法, 证明了热平衡稳态解的存在唯一性.然后, 得到了Cauchy-Neumann问题光滑解的整体存在性以及当t→ +∞这种光滑解以指数速度收敛到稳定解, 改进了文献[12]的结果.In this paper,we investigate a three-dimensional nonisentropic hydrodynamic model for semiconductors.By using energy estimates,we first prove the existence and uniqueness of solution for the corresponding thermal-equilibrium steady state.Then,when the initial data are close to the thermal-equilibrium steady state,we show the global existence of smooth solutions for the Cauchy-Neumann problem in a bounded domain.We also show that,as t → ＋∞,the solutions converge to the thermal-equilibrium steady state exponentially fast.The steady state and the doping profile are permitted to be of large variation but the initial velocity must be small,which improve the results of [12].

关 键 词：全局存在性 热平衡稳定状态 非等熵的 流体动力学模型 能量估计 

分 类 号：O175.2[理学—数学]