| 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. |
| 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 |
| DOI： |
| 分类号:O175.29 |
| 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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| WEAK SOLUTIONS TO STATIONARY BIPOLARQUANTUM DRIFT-DIFFUSION MODEL IN ONESPACE DIMENSION |
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DONG Jian-wei, MAO Bei-xing
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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. |
| Key words: quantum drift-difiusion model stationary solutions existence uniqueness semiclassical limit |
