三维双极Euler-Poisson方程初值问题光滑解的整体存在性和渐近性  

Global Existence and Asymptotic Behavior of Smooth Solutions to the IBVP for the 3D Bipolar Euler-Poisson System

作　　者：毛剑峰[1] 黎野平[2] 

机构地区：[1]湖北科技学院数学与统计学院湖北咸宁437100 [2]上海师范大学数学系上海200234

出　　处：《数学物理学报（A辑）》2013年第3期510-522,共13页Acta Mathematica Scientia

基　　金：国家自然科学基金(11171223);上海市教委创新重点项目(13ZZ109)资助

摘　　要：研究了一类来白于半导体和等离子体中的三维双极Euler-Poisson方程(流体力学模型),该方程具有由带有电场和摩擦阻尼项的动量方程的Euler-Poisson形式.首先证明了带有滑动边界条件和Nemann边界条件的初边值问题的经典解的整体存在性和唯一性;其次,也证明了三维双极Euler-Poisson方程的初边值问题的解的渐近性.即两个粒子的密度满足多孔介质方程的相应解,且相应的动量满足Darcy律.In this paper, we study a three-dimensional （3D） bipolar Euler-Poisson system （hydrodynamic model） from semiconductors and plasmas. This system takes the form of Euler- Poisson with electric field and frictional damping added to the momentum equations. We first proved global existence and uniqueness of classical solutions to the initial boundary value problem （IBVP） with slip boundary condition and Nemann boundary condition when the initial data is near its equilibrium. As the by-product, we also show asymptotic behavior of IBVP for the three-dimensional bipolar Euler-Poisson system. That is, the density of two particles （electron and hole or positive and negative ion） is verified to satisfy the porous medium equation and the current momentums obey to the classical Darcy＇s law.

关 键 词：整体存在性 双极 EULER-POISSON方程 能量估计 渐近性 

分 类 号：O175.2[理学—数学]