摘要
本文研究了半导体中一维双极量子漂移–扩散稳态模型的弱解.利用指数变换法把此模型转化成两个四阶椭圆方程,然后利用Schauder不动点定理证明了转化后的方程组弱解的存在性.另外得到了方程组解的唯一性和半古典极限.
In this paper, we study the weak solutions to stationary bipolar quantum driftdiffusion model for semiconductors in one space dimension. The model is reformulated as two coupled fourth-order elliptic equations by using exponential variable transformations. The existence of weak solutions to the reformulated equations is proved by using Schauder fixed-point theorem. Furthermore, the uniqueness of solutions and the semiclassical limit to the equations are obtained.
出处
《数学杂志》
CSCD
北大核心
2015年第3期530-538,共9页
Journal of Mathematics
基金
Supported by the Vital Science Research Foundation of Henan Province Education Department(12A110024)
the Youth Natural Science Foundation of Zhengzhou Institute of Aeronautical Industry Management(2013111001)
the Natural Science Foundation of Henan Province Science and Technology Department(132300410373)
关键词
量子漂移-扩散模型
稳态解
存在性
唯一性
半古典极限
quantum drift-diffusion model
stationary solutions
existence
uniqueness semiclassical limit
