ASYMPTOTIC BEHAVIORS AND CLASSICAL LIMITS OF SOLUTIONS TO A QUANTUM DRIFT-DIFFUSION MODEL FOR SEMICONDUCTORS
ASYMPTOTIC BEHAVIORS AND CLASSICAL LIMITS OF SOLUTIONS TO A QUANTUM DRIFT-DIFFUSION MODEL FOR SEMICONDUCTORS
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DOI：
10.1142/s0218202510004477
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发表时间：
2010-06
影响因子：
3.5
通讯作者：
S. Nishibata;Naotaka Shigeta;Masahiro Suzuki
中科院分区：
文献类型：
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作者：
S. Nishibata;Naotaka Shigeta;Masahiro Suzuki
讨论了一维有界区域上半导体量子漂移扩散模型初边值问题解的时间整体存在性、渐近性态和奇异极限.首先，我们证明了该模型平稳解的存在唯一性和渐近稳定性。其次，证明了当标度普朗克常数趋于零时，量子漂移扩散模型的时间整体解收敛于漂移扩散模型的时间整体解。这种奇异极限称为经典极限。在这里，这些定理允许初始数据在适当的Sobolev空间中任意大。我们用能量法证明了它们。
This paper discusses a time global existence, asymptotic behavior and a singular limit of a solution to the initial boundary value problem for a quantum drift-diffusion model of semiconductors over a one-dimensional bounded domain. Firstly, we show a unique existence and an asymptotic stability of a stationary solution for the model. Secondly, it is shown that the time global solution for the quantum drift-diffusion model converges to that for a drift-diffusion model as the scaled Planck constant tends to zero. This singular limit is called a classical limit. Here these theorems allow the initial data to be arbitrarily large in the suitable Sobolev space. We prove them by applying an energy method.