中文摘要：

该文考察源自半导体材料科学中的双极非等熵Euler-Poisson方程组.运用对称子的技巧与时空混合导数迭代方法,研究了三维空间环上的周期问题.在初值为一个非常数平衡解的小摄动条件下,证明了当时间趋于无穷大时,该问题存在唯一整体光滑解,且按指数速率收敛至平衡态.这种粒子输运现象反映了双极非等熵与单极非等熵、双极等熵Euler-Poisson方程组之间存在本质区别.

英文摘要：

This article is concerned with the bipolar non-isentropic Euler-Poisson equations in semiconductors.We investigated,by means of an induction argument on the order of the mixed time-space derivatives of solutions in energy estimates and the techniques of symmetrizer,the periodic problem in a three-dimensional torus.Under the assumption that initial data are close to a non constant equilibrium solutions,we prove that the smooth solutions of this problem converge to a steady state with exponential decay rates as the time goes to the infinity.This phenomenon on the charge transport shows the essential difference among the bipolar nonisentropic,the unipolar non-isentropic and the bipolar isentropic Euler-Poisson equations.