Quasineutral Limit of Isothermalk Quantum Hydrodynamic Model

董建伟; 娄光谱

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Quasineutral Limit of Isothermalk Quantum Hydrodynamic Model

更新时间：2026-09-14

- Quasineutral Limit of Isothermalk Quantum Hydrodynamic Model
- 量子流体动力学等温模型的拟中性极限
- Vol. 33, Issue 2, Pages: 102-106(2012)
- 作者机构：
  
  郑州航空工业管理学院数理系
- 作者简介：
- 基金信息：
- DOI：
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- Published：2012
- 稿件说明：
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董建伟, 娄光谱. Quasineutral Limit of Isothermalk Quantum Hydrodynamic Model[J]. 2012, 33(2): 102-106.
DOI：

董建伟, 娄光谱. Quasineutral Limit of Isothermalk Quantum Hydrodynamic Model[J]. 2012, 33(2): 102-106. DOI：

摘要

研究三维量子流体动力学等温模型

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、电子速度以及静电场位势之间的非线性关系.该模型中含有非线性三阶导数项

这在数学上给研究该模型带来了困难.在周期边界条件下

利用能量泛函方法和弱收敛紧性方法证明了当德拜长度趋于零时其光滑解收敛于不可压缩方程的强解

Abstract

The isothermal quantum hydrodynamic model in three dimensional space is investigated.The model is one of the quantum macroscopic models used to simulate the quantum effects in miniaturized semiconductor devices

and it reflects the nonlinear relation among the electron density

the electron velocity and the electrostatic potential.The model contains a nonlinear third-order derivative item

which induces mathematical difficulties.By using the energy functional method and the weak convergence compactness method

the smooth solution of the model converges to the strong solution of incompressible Euler equations is proved under periodic boundary conditions.

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references

Li HL,Marcati P.Existence and asymptotic behavior of multi-dimentional quantum hydrodynamic model for semiconductors[J].Communications in Mathematical Physics,2004,245:215-247.

Jüngel A,Li H L.Quantum Euler-Poisson systems:global existence and exponential decay[J].Quart.Appl.Math.,2004,62:569-600.

Huang F M,Li H L,Matsumura A.Existence and stability of steady-state of one-dimensional quantum hydrodynamic system for semiconductors[J].Journal of Differential Equations,2006,225:1-25.

Jüngel A,Li HL,Matsumura A.The relaxation-time limit in the quantum hydrodynamic equations for semiconductors[J].Journal of Differential Equations,2006,225:440-464.

Nishibata S,Suzuki M.Initial boundary value pro-blems for a quantum hydrodynamic model of semiconductors[J].Journal of Differential Equations,2008,244:836-874.

Li HL,Lin Chikun.Zero Debye length asym-ptotic of the quantum hydrodynamic model for semiconductors[J].Communications in Mathematical Physics,2005,256(1):195-212.

Lions P L.Mathematical Topics in Fluid Mechanics,Vol1:Incompressible Models[M].New York:The Clarendon Press,Oxford University Press,1996.

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