[1] Jiang Weixiang, Guan Ping,. Weak solutions to one-dimensional quantum drift-diffusionequations for semiconductors [J]. Journal of Southeast University (English Edition), 2006, 22 (4): 577-581. [doi:10.3969/j.issn.1003-7985.2006.04.027]

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Weak solutions to one-dimensional quantum drift-diffusionequations for semiconductors()

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

22

Issue:

2006 4

Page:

577-581

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2006-12-30

Info

Title:

Weak solutions to one-dimensional quantum drift-diffusionequations for semiconductors

Author(s):

Jiang Weixiang;  Guan Ping

School of Sciences, Southeast University, Nanjing 210096, China

Keywords:

semiconductor device;  quantum drift-diffusion equations;  existence and uniqueness;  exponential variable transformation;  semiclassical limit

PACS:

O29

DOI:

10.3969/j.issn.1003-7985.2006.04.027

Abstract:

The weak solutions to the stationary quantum drift-diffusion equations(QDD)for semiconductor devices are investigated in one space dimension.The proofs are based on a reformulation of the system as a fourth-order elliptic boundary value problem by using an exponential variable transformation.The techniques of a priori estimates and Leray-Schauder’s fixed-point theorem are employed to prove the existence.Furthermore, the uniqueness of solutions and the semiclassical limit δ→0 from QDD to the classical drift-diffusion(DD)model are studied.

References:

[1] Guan Ping, Fan Jishan.On the global existence and uniqueness of weak solutions to nonstationary semiconductor equations[J].Applied Mathematics and Computation, 2000, 114(2, 3):125-133.
[2] Fan Jishan, Wu Hongwei.On the N-dimensional stationary drift-diffusion semiconductor equations[J].Nonlinear Analysis, 2001, 43(1):127-135.
[3] Fang W, Ito K.On the time-dependent drift-diffusion model for semiconductors[J].J of Diff Eqs, 1995, 117(2):245-280.
[4] Jüngel A.Nonlinear problems in quantum semiconductor modeling[J]. Nonlinear Analysis, 2001, 47(9):5873-5884.
[5] Abdallah N Ben, Unterreiter A.On the stationary quantum drift-diffusion model[J].Z Angew Math Phys, 1998, 49(2):251-275.
[6] Jüngel A, Li H L, Markowich P, et al.Recent progress on quantum hydrodynamic models for semiconductors[A].In:Hyperbolic Problems:Theory, Numerics, Applications[C].Berlin: Springer, 2003.217-226.
[7] Jüngel Ansgar, Li Hailiang.Quantum Euler-Poisson systems:existence of stationary states[J].Archivum Mathematicum (BRNO), 2004, 40(4):435-456.
[8] Gualdani M P, Jüngel A.Analysis of the viscous quantum hydrodynamic equations for semiconductors[J].Europ J Appl Math, 2004, 15(5):577-595.
[9] Troianiello G M.Elliptic differential equations and obstacle problems[M]. Plenum Press, 1987.
[10] Gilbarg D, Trudinger N S.Elliptic partial differential equations of second order[M]. 2nd ed. Springer-Verlay, 1983.

Memo

Memo:

Biographies: Jiang Weixiang(1981—), male, graduate;Guan Ping(corresponding author), male, professor, pguan@seu.edu.cn.

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