| 一维双极量子漂移-扩散稳态模型的弱解 |
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| 引用本文： | 董建伟,毛北行.一维双极量子漂移-扩散稳态模型的弱解[J].数学杂志,2015,35(3):530-538. |
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| 作者姓名： | 董建伟 毛北行 |
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| 作者单位： | 郑州航空工业管理学院数理系, 河南 郑州 450015,郑州航空工业管理学院数理系, 河南 郑州 450015 |
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| 基金项目： | 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) and the Natural Science Foundation of Henan Province Science and Technology Department (132300410373). |
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| 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.
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| 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 |
| 收稿时间： | 2013/4/8 0:00:00 |
| 修稿时间： | 2013/9/5 0:00:00 |
WEAK SOLUTIONS TO STATIONARY BIPOLARQUANTUM DRIFT-DIFFUSION MODEL IN ONESPACE DIMENSION |
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| DONG Jian-wei and MAO Bei-xing.WEAK SOLUTIONS TO STATIONARY BIPOLARQUANTUM DRIFT-DIFFUSION MODEL IN ONESPACE DIMENSION[J].Journal of Mathematics,2015,35(3):530-538. |
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| Authors: | DONG Jian-wei and MAO Bei-xing |
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| Institution: | Dpt. of Math. and Phys., Zhengzhou Institute of Aeronautical Industry Management, Zhengzhou 450015, China and Dpt. of Math. and Phys., Zhengzhou Institute of Aeronautical Industry Management, Zhengzhou 450015, China |
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| Abstract: | In this paper, we study the weak solutions to stationary bipolar quantum driftdifiusion 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 flxed-point theorem. Furthermore, the uniqueness of solutions and the semiclassical limit to the equations are obtained. |
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| Keywords: | quantum drift-difiusion model stationary solutions existence uniqueness semiclassical limit |
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