半导体技术中数学模型的渐近分析

Asymptotic Analysis of the Mathematical Model in the Semiconductor Technology

本文在非平衡状态下 ,研究了具有 Dirichlet边界条件的稳态半导体模型的解的渐近性态 .首先 ,对 N维半导体模型 ,结合解在 L∞ 和 H1 空间一致有界性 ,论证了奇异摄动问题的解的极限满足相应的退化问题且在 H1 中弱收敛 .然后 ,对一维半导体模型 ,进一步证明了解在 H 1中强收敛 .

In this paper, the asymptotic behaviour of the solution for the steady state semiconductor device equations with the Dirichlet condition is concerned when R≠0. At first, in N dimensional case, using uniform boundedness of the solution in L ∞(Ω) and in H 1(Ω), 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)