一维双极量子漂移-扩散稳态模型的弱解（英文）  

WEAK SOLUTIONS TO STATIONARY BIPOLAR QUANTUM DRIFT-DIFFUSION MODEL IN ONE SPACE DIMENSION

作　　者：董建伟[1] 毛北行[1] 

机构地区：[1]郑州航空工业管理学院数理系,河南郑州450015

出　　处：《数学杂志》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)

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.

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 

分 类 号：O175.29[理学—数学]