|
|
|
Quasineutral limit of bipolar quantum hydrodynamic model for semiconductors |
Xiuhui YANG( ) |
| Department of Mathematics, College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China |
|
|
|
|
Abstract This paper is concerned with the quasineutral limit of the bipolar quantum hydrodynamic model for semiconductors. It is rigorously proved that the strong solutions of the bipolar quantum hydrodynamic model converge to the strong solution of the so-called quantum hydrodynamic equations as the Debye length goes to zero. Moreover, we obtain the convergence of the strong solutions of bipolar quantum hydrodynamic model to the strong solution of the compressible Euler equations with damping if both the Debye length and the Planck constant go to zero simultaneously.
|
| Keywords
Bipolar quantum hydrodynamic model
quantum hydrodynamic equations
compressible Euler equations
quasineutral limit
modulated energy functional
|
|
Corresponding Author(s):
YANG Xiuhui,Email:nuaaxh@yahoo.com.cn
|
|
Issue Date: 01 April 2011
|
|
| 1 |
Antonelli P, Marcati P. On the finite energy weak solutions to a system in quantum fluid dynamics. Comm Math Phys , 2009, 287: 657-686
doi: 10.1007/s00220-008-0632-0
|
| 2 |
Brenier Y. Convergence of the Vlasov-Poisson system to the incompressible Euler equations. Comm Partial Differential Equations , 2000, 25: 737-754
doi: 10.1080/03605300008821529
|
| 3 |
Gamba I M, Gualdani M P, Zhang P. On the blowing up of solutions to quantum hydrodynamic models on bounded domains. Monatsh Math , 2009, 157: 37-54
doi: 10.1007/s00605-009-0092-4
|
| 4 |
Gasser I, Marcati P. A quasi-neutral limit in a hydrodynamic model for charged fluids. Monatsh Math , 2003, 138: 189-208
doi: 10.1007/s00605-002-0482-3
|
| 5 |
Hsiao L, Li H L. The well-posedness and asymptotics of multi-dimensional quantum hydrodynamics. Acta Math Sci, Ser B , 2009, 29: 552-568
|
| 6 |
Hsiao L, Wang S. Quasineutral limit of a time-dependent drift-diffusion-Poisson model for pn junction semiconductor devices. J Differential Equations , 2006, 225: 411-439
doi: 10.1016/j.jde.2006.01.022
|
| 7 |
Jia Y L, Li H L. Large-time behavior of solutions of quantum hydrodynamic model for semiconductors. Acta Math Sci, Ser B , 2006, 26: 163-178
|
| 8 |
Jüngel A. Quasi-hydrodynamic Semiconductor Equations. Progress in Nonlinear Differential Equations and Their Applications, Vol 41 . Basel: Birkh?user Verlag, 2001
|
| 9 |
Jüngel A, Li H L. Quantum Euler-Poisson systems: global existence and exponential decay. Quart Appl Math , 2004, 62: 569-600
|
| 10 |
Jüngel A, Li H L, Matsumura A. The relaxation-time limit in the quantum hydrodynamic equations for semiconductors. J Differential Equations , 2006, 225: 440-464
doi: 10.1016/j.jde.2005.11.007
|
| 11 |
Jüngel A, Mariani M C, Rial D. Local existence of solutions to the transient quantum hydrodynamic equations. Math Models Methods Appl Sci , 2002, 12: 485-495
doi: 10.1142/S0218202502001751
|
| 12 |
Jüngel A, Violet I. The quasineutral limit in the quantum drift-diffusion equations. Asympt Anal , 2007, 53: 139-157
|
| 13 |
Li F C. Quasineutral limit of the viscous quantum hydrodynamic model for semiconductors. J Math Anal Appl , 2009, 352: 620-628
doi: 10.1016/j.jmaa.2008.11.011
|
| 14 |
Li H L, Marcati P. Existence and asymptotic behavior of multi-dimensional quantum hydrodynamic model for semiconductors. Comm Math Phys , 2004, 245: 215-247
doi: 10.1007/s00220-003-1001-7
|
| 15 |
Li H L, Zhang G J, Zhang K J. Algebraic time decay for the bipolar quantum hydrodynamic model. Math Models Methods Appl Sci , 2008, 18: 859-881
doi: 10.1142/S0218202508002887
|
| 16 |
Liang B, Zhang K J. Steady-state solutions and asymptotic limits on the multidimensional semiconductor quantum hydrodynamic model. Math Models Methods Appl Sci , 2007, 17: 253-275
doi: 10.1142/S0218202507001905
|
| 17 |
Lin C K, Li H L. Zero Debye length asymptotic of the quantum hydrodynamic model for semiconductors. Comm Math Phys , 2005, 256: 195-212
doi: 10.1007/s00220-005-1316-7
|
| 18 |
Nishibata S, Suzuki M. Initial boundary value problems for a quantum hydrodynamic model of semiconductors: asymptotic behaviors and classical limits. J Differential Equations , 2008, 244: 836-874
doi: 10.1016/j.jde.2007.10.035
|
| 19 |
Sideris C, Thomases B, Wang D. Long time behavior of solutions to the 3D compressible Euler equations with damping. Comm Partial Differential Equations , 2003, 28: 953-978
doi: 10.1081/PDE-120020497
|
| 20 |
Unterreiter A. The thermal equilibrium solution of a generic bipolar quantum hydrodynamic model. Comm Math Phys , 1997, 188: 69-88
doi: 10.1007/s002200050157
|
| 21 |
Ri J, Huang F M. Vacuum solution and quasineutral limit of semiconductor driftdiffusion equation. J Differential Equations , 2009, 246: 1523-1538
doi: 10.1016/j.jde.2008.10.013
|
| 22 |
Wang S, Xin Z P, Markowich P A. Quasineutral limit of the drift diffusion models for semiconductors: The case of general sign-changing doping profile. SIAM J Math Anal , 2006, 37: 1854-1889
doi: 10.1137/S0036141004440010
|
| 23 |
Zhang B, Jerome J W. On a steady-state quantum hydrodynamic model for semiconductors. Nonlinear Anal , 1996, 26: 845-856
doi: 10.1016/0362-546X(94)00326-D
|
| 24 |
Zhang G J, Li H L, Zhang K J. Semiclassical and relaxation limits of bipolar quantum hydrodynamic model for semiconductors. J Differential Equations , 2008, 245: 1433-1453
doi: 10.1016/j.jde.2008.06.019
|
| 25 |
Zhang G J, Zhang K J. On the bipolar multidimensional quantum Euler-Poisson system: The thermal equilibrium solution and semiclassical limit. Nonlinear Anal , 2007, 66: 2218-2229
doi: 10.1016/j.na.2006.03.010
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
| |
Shared |
|
|
|
|
| |
Discussed |
|
|
|
|
