| 摘要: |
| 研究了来自于半导体器件和等离子体中的一维双极量子漂移-扩散模型的稳态解.在有合适边界条件的有界区域里,先利用Schauder不动点定理和能量估计的技巧，证明一维双极量子漂移-扩散模型的稳态解的存在性和唯一性;其次,研究双极量子漂移-扩散模型的稳态解的经典极限,即当普朗克常数ε趋于零时,量子漂移-扩散模型的稳态解趋向于经典漂移-扩散模型的稳态解. |
| 关键词: 存在性 唯一性 经典极限 |
| DOI： |
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| Existence and classical limit of stationary solutions to a one dimensional bipolar quantum drift diffusion equation |
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YANG Ting, LI Yeping
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College of Mathematics and Sciences,Shanghai Normal University
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| Abstract: |
| We study the stationary solutions of a one-dimensional bipolar quantum drift-diffusion model from semiconductor devices and plasmas. In a bounded interval supplemented by the proper boundary conditions,we first show the existence and uniqueness of the stationary solutions to the one-dimensional bipolar quantum drift-diffusion model. The proof can be completed by the Schauder fixed-point principle and the careful energy estimates. Then,we study the classical limit of the stationary solutions to the bipolar quantum drift-diffusion model. Namely,we show that the stationary solution to the quantum drift-diffusion model approaches that to the drift-diffusion model as the scaled Planck constant ε tends to zero. |
| Key words: existence uniqueness classical limit |
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