半导体飘流扩散方程组初边值问题解的渐近性

针对半导体材料中飘流扩散方程组初边值问题解的渐近性,提出了在Doping轮廓和适当的初值假设下,发展问题的光滑解能够以较快的收敛速度指数衰减到相应的平衡解,并证明了该问题的收敛性.证明中,通过估计二阶导数的L2范数去掉了压力函数需满足其一阶导数大于0、三阶导数小于0的假设条件,从而对非单调、非三阶光滑的压力函数同样适用.在常数Doping轮廓下,把单极情形下飘流扩散方程组初边值问题解的渐近性推广到双极情形.

Asymptotic Discussion of the Solutions to the Initial Boundary Value Problem for Semiconductors Drift Diffusion Equations

The asymptotic behaviours of the solutions to the initial boundary value problem for semiconductors drift diffusion equations are investigated. Under the proper assumptions on doping profile and initial value, the smooth solution to the evolutionary problems more rapidly tends to the unique stationary solution exponentially as time reaches to infinity, and the convergence of this problem is proved simultaneously. Some of hypotheses for the press function are weakened via estimating the nom .L~2., the practical application is widened obviously, and under the constant doping profile, the asymptotic behaviours can be extended to apply in a bipolar situation.