Unique Existence And Asymptotic Analysis Of Steady - State Solutions For A Class Of High - Dimensional Bipolar Non - Isentropic Euler - Poisson Equations

In this thesis,I mainly discuss the hydrodynamic model from semiconductor devices,which consists of conservation law of mass,momentum,energy and the Poisson equation.For the proper boundary conditions,we are interested in the unique existence of stationary solutions and relative limit analysis.Firstly§by means of the standard theory of the second elliptic equations,Schauder fixed point theorem,the Stampacchia’s truncation method and elaborate energy estimates,we prove the unique existence of stationary solutions.Secondly,we investigate the zero-electron-mass limit, the zero-relaxation-time limit and the Debye-length(quasi-neutral) limit for the stationary solutions, respectively. For each limit, we show the strong convergence of the sequence of solutions and give the associated convergence rates.In Chapter one, we introduce the background of our research and main topics that we will study in the following chapters.In Chapter two, we state some necessary basic knowledge and some theorems that will be used in our research.In Chapter three, we firstly establish the stationary solution of a multi-dimensional bipolar Euler-Poisson equations with proper boundary conditions,then show the existence of the smooth solutions under the Schauder fixed point theorem and the standard theory of the second elliptic equations.In Chapter four, We mainly investigate the zero-electron-mass limit, the zero-relaxationtime limit and the Debye-length(quasi-neutral) limit for the stationary solutions, respectively. For each limit, we show the strong convergence of the sequence of solutions and give the associated convergence rates.