论文标题
半导体流体动力模型的凯奇问题的全球解决方案和放松限制
Global solutions and Relaxation Limit to the Cauchy Problem of a Hydrodynamic Model for Semiconductors
论文作者
论文摘要
众所周知，由于缺乏一项技术，可以获得一维欧拉（Cauchy）问题的人工粘度解决方案的A-Priori $ l^{\ infty} $估计，用于一维欧拉（Euler-Poisson）（或流体动力学）模型的半导体模型，用于半导体，通过使用压力密度的三个模型，该模型被以过去的三个模型而替换了，以上三个模型，以过去的三个模型，这些模型均通过了三个改进，所有这些模型均通过朝外的方式替换为所有的使用。初始价值问题\ cite {zh1，li}和cauchy问题\ cite \ cite {mn1，prv，prv，hly}的lax-friedrichs，godounov计划和GLIMM方案;或通过使用消失的人工粘度法来解决初始有限值问题\ cite {jo，hlyy}。在本文中，通过使用消失的人工粘度法证明了对于该模型的库奇问题而存在的全球熵解决方案的存在。作为副产品，应用已知的紧凑型框架\ cite {mn2，jr}用于显示放松限制，因为关系时间$τ$和$ \ e，δ$，对于一般压力$ p（ρ）$。
It is well-known that due to the lack of a technique to obtain the a-priori $L^{\infty}$ estimate of the artificial viscosity solutions of the Cauchy problem for the one-dimensional Euler-Poisson (or hydrodynamic) model for semiconductors, where the energy equation is replaced by a pressure-density relation, over the past three decades, all solutions of this model were obtained by using the Lax-Friedrichs, Godounov schemes and Glimm scheme for both the initial-boundary value problem \cite{Zh1,Li} and the Cauchy problem \cite{MN1,PRV,HLY}; or by using the vanishing artificial viscosity method for the initial-boundary value problem \cite{Jo,HLYY}. In this paper, the existence of global entropy solutions, for the Cauchy problem of this model, is proved by using the vanishing artificial viscosity method. As a by-product, the known compactness framework \cite{MN2,JR} is applied to show the relaxation limit, as the relation time $ τ$ and $\E,δ$ go to zero, for general pressure $P(ρ)$.
