半导体非等熵Euler-Poisson系统非常数平衡解的稳定性

Stability of non-constant steady state solutions for non-isentropic Euler-Poisson system in semiconductors

本文考虑源自半导体材料科学中的非等熵可压缩Euler-Poisson系统.借助时空混合导数迭代方法和对称子技巧,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态的小摄动前提下,证明了当时间趋于无穷大时,该问题的整体光滑解按指数速率衰减至平衡态.这种粒子输运现象反映了等熵与非等熵系统的本质联系.

This work is concerned with the non-isentropic EuleroPoisson system in semiconductors. We investigate, by means of the techniques of symmetrizer and an induction argument on the order of the mixed time-space derivatives of solutions in energy estimates, the periodic problem in a three-dimensional torus. Under the assumption that the initial data is close to a non-constant steady state 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 relation between the isentropic and the non-isentropic compressible Euler-Poisson system.