当前位置: X-MOL 学术Z. Angew. Math. Phys. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
The existence, uniqueness and exponential decay of global solutions in the full quantum hydrodynamic equations for semiconductors
Zeitschrift für angewandte Mathematik und Physik ( IF 2 ) Pub Date : 2021-04-30 , DOI: 10.1007/s00033-021-01540-8
Sungjin Ra , Hakho Hong

In this paper, we are concerned with the large-time behavior of the solutions in the full quantum hydrodynamic model, which can be used to analyze the thermal and quantum influences on the transport of carriers (electrons or holes) in semiconductor device. For the Cauchy problem in \({\mathbb {R}}^3\), the global existence and uniqueness of smooth solutions, when the initial data are small perturbations of an equilibrium state, are obtained. Also, the solutions tend to the corresponding equilibrium state exponentially fast as the time tends to infinity. The analysis is based on the elementary \(L^2\)-energy method, but various techniques are introduced to establish a priori estimates.



中文翻译:

半导体全量子流体动力学方程中整体解的存在性,唯一性和指数衰减

在本文中,我们关注全量子流体动力学模型中解的长时间行为,该行为可用于分析热和量子对半导体器件中载流子(电子或空穴)传输的影响。对于\({{mathbb {R}} ^ 3 \)中的柯西问题,当初始数据为平衡态的小扰动时,可获得光滑解的整体存在性和唯一性。同样,随着时间趋于无穷大,解会以指数形式快速地趋向于相应的平衡状态。该分析基于基本\(L ^ 2 \)-能量方法,但是引入了各种技术来建立先验估计。

更新日期:2021-04-30
down
wechat
bug