非平衡状态下半导体方程解在H^1中的收敛  

CONVERGENCE IN H^1 OF UNEQUILIBRIUM SOLUTIONS FOR THE STEADY STATE SEMICONDUCTOR DEVICE EQUATIONS

作　　者：许立炜[1] 

机构地区：[1]南京邮电学院应用数理系,南京210003

出　　处：《应用数学学报》2002年第2期312-317,共6页Acta Mathematicae Applicatae Sinica

摘　　要：本文研究具有Dirichlet边界条件的稳态半导体模型,在净复合率R≠0时,对N维半导体方程,论证了奇异摄动问题的解在H1中弱收敛于退化问题的解;对一维半导体模型,进一步证明了解在H1中强收敛.Abstract In this paper, the steady state semiconductor device equations with the Dirichlet condition are concerned when R≠0. At first, in N-dimensional case, we show that the limit of solutions of the singular perturbation problem is a solution of reduced problem and the convergence holds weakly in H^(1)(Ω). Then, in one-dimensional case, we prove the convergence holds strongly in H^(1)(Ω).

关 键 词：半导体方程 解 收敛 非线性偏微分方程 奇异摄动 渐近性态 

分 类 号：TN302[电子电信—物理电子学] O175.2[理学—数学]