The stationary solution of a one-dimensional bipolar quantum hydrodynamic model

被引：5

作者：

Hu, Jing ^{[1
]}

Li, Yeping ^{[2
]}

Liao, Jie ^{[1
]}

机构：

[1] East China Univ Sci & Technol, Sch Sci, Shanghai 200237, Peoples R China

[2] Nantong Univ, Sch Sci, Nantong 226019, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2021年 / 493卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Bipolar quantum hydrodynamic model; Stationary solution; Existence; Uniqueness; LARGE-TIME BEHAVIOR; STEADY-STATE SOLUTIONS; ASYMPTOTIC-BEHAVIOR; SEMICONDUCTORS; EXISTENCE; EQUATIONS;

D O I：

10.1016/j.jmaa.2020.124537

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the existence and uniqueness of stationary solution to the bipolar quantum hydrodynamic model in one dimensional space with general non constant doping profile. The existence of the stationary solution is proved by LeraySchauder fixed-point theorem and a crucial truncation technique is used to derive the positive upper and lower bounds of the stationary solution. The uniqueness of the stationary solution is shown by a delicate energy estimate. (c) 2020 Elsevier Inc. All rights reserved.

引用

页数：15

共 32 条

[1] On a hierarchy of macroscopic models for semiconductors [J].

BenAbdallah, N ;

Degond, P .

JOURNAL OF MATHEMATICAL PHYSICS, 1996, 37 (07) :3306-3333

[2]

Degond P., 1990, Appl. Math. Lett., V3, P25, DOI DOI 10.1016/0893-9659(90)90130-4

[3] Steady states and interface transmission conditions for heterogeneous quantum-classical 1-D hydrodynamic model of semiconductor devices [J].

Di Michele, F. ;

Marcati, P. ;

Rubino, B. .

PHYSICA D-NONLINEAR PHENOMENA, 2013, 243 (01) :1-13

[4] Stationary solutions for a new hybrid quantum model for semiconductors with discontinuous pressure functional and relaxation time [J].

Di Michele, Federica ;

Mei, Ming ;

Rubino, Bruno ;

Sampalmieri, Rosella .

MATHEMATICS AND MECHANICS OF SOLIDS, 2019, 24 (07) :2096-2115

[5] Thermal equilibrium solution to new model of bipolar hybrid quantum hydrodynamics [J].

Di Michele, Federica ;

Mei, Ming ;

Rubino, Bruno ;

Sampalmieri, Rosella .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2017, 263 (03) :1843-1873

[6]

Di Michele F, 2016, INT J NUMER ANAL MOD, V13, P898

[7] Asymptotic behavior of solutions to Euler-Poisson equations for bipolar hydrodynamic model of semiconductors [J].

Donatelli, Donatella ;

Mei, Ming ;

Rubino, Bruno ;

Sampalmieri, Rosella .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2013, 255 (10) :3150-3184

[8] Steady-state solutions of a one-dimensional hydrodynamic model for semiconductors [J].

Fang, WF ;

Ito, K .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1997, 133 (02) :224-244

[9]

GAMBA IM, 1992, COMMUN PART DIFF EQ, V17, P553

[10]

Gamba IM, 2001, ARCH RATION MECH AN, V156, P183, DOI 10.1007/s002050100114

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