| 量子漂移-扩散等温模型解的长时间性质 |
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| 引用本文： | 董建伟,程春蕊. 量子漂移-扩散等温模型解的长时间性质[J]. 四川师范大学学报(自然科学版), 2011, 34(1): 139-142. DOI: 10.3969/j.issn.1001-8395.2011.01.027 |
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| 作者姓名： | 董建伟 程春蕊 |
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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 |
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| 基金项目： | 河南省高等学校青年骨干教师资助计划基金(2006110016)资助项目 |
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| 摘 要： | 研究一维单极量子漂移-扩散等温模型,它是用来模拟超小半导体器件发生量子效应的宏观量子模型之一,反映了电子浓度与静电场位势之间的非线性关系.量子漂移-扩散模型与经典漂移-扩散模型的区别在于前者包含了量子校正项.从数学的角度讲,此模型是由一个非线性四阶抛物方程与一个泊松方程耦合而成的方程组.研究此模型的困难在于非线性四阶抛物方程缺少极大值原理.利用对数索伯列夫不等式与能量估计的方法,在周期边界条件下,证明了当时间趋于无穷大时此模型的解以指数函数的速度趋于它的平均值.
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| 关 键 词： | 量子漂移-扩散等温模型 周期边界 弱解 长时间性质 |
Long-time Property of the Solution for Isothermal Quantum Drift-diffusion Model |
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| DONG Jian-wei,CHENG Chun-rui. Long-time Property of the Solution for Isothermal Quantum Drift-diffusion Model[J]. Journal of Sichuan Normal University(Natural Science), 2011, 34(1): 139-142. DOI: 10.3969/j.issn.1001-8395.2011.01.027 |
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| Authors: | DONG Jian-wei CHENG Chun-rui |
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| Affiliation: | DONG Jian-wei,CHENG Chun-rui(Department of Mathematics and Physics,Zhengzhou Institute of Aeronautical Industry Management,Zhengzhou 450015,Henan) |
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| Abstract: | The one-dimensional unipolar isothermal quantum drift-diffusion model is investigated,which is one of the quantum macroscopic models used to simulate the quantum effects in superminiature semiconductor devices.The model reflects the nonlinear relation between the electron density and the electrostatic potential.The difference between the quantum and the classical drift-diffusion models is that the former includes the quantum correction term.Mathematically,the model is a system which consists of a nonlinear ... |
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| Keywords: | isothermal quantum drift-diffusion model periodic boundary weak solution long-time property |
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