| [1] |
Cimartti G. Invariant regions for the Nernst-Planck equations. Ann Mat Pura Appl, 1998, 175: 93-118
doi: 10.1007/BF01783677
|
| [2] |
Rubinstein I. Electro-Diffusion of Ions. Philadelphia: Siam, 1990
|
| [3] |
Li F C. Quasi-neutral limit of the electro-diffusion model arising in electrohydrodynamics. J Diff Equations, 2009, 246: 3620-3641
doi: 10.1016/j.jde.2009.01.027
|
| [4] |
Wang S, Jiang L M, Liu C D. Quasi-neutral limit and the boundary layer problem of Planck Nernst Poisson Navier Stokes equations for electro hydrodynamics. J Diff Equations, 2009, 267: 3475-3523
doi: 10.1016/j.jde.2019.04.011
|
| [5] |
Wang S, Jiang L M. Quasi-neutral limit and the boundary layer problem of the electro diffusion model arising in electro hydrodynamics. Nonlinear Anal: RWA, 2021, 59: 103266
doi: 10.1016/j.nonrwa.2020.103266
|
| [6] |
Yang J W, Ju Q C. Convergence of the quantum Navier-Stokes-Poisson equations to the incompressible Euler equations for general initial data. Nonlinear Anal: RWA, 2015, 23: 148-159
doi: 10.1016/j.nonrwa.2014.12.003
|
| [7] |
Liu C, Wang Y, Yang T. On the ill-posedness of the prandtl equations in three-dimensional space. Arch Ration Mech Anal, 2016, 220: 83-108
doi: 10.1007/s00205-015-0927-1
|
| [8] |
Brenier Y. Convergence of the Vlasov-Poisson system to the incompressible Euler equations. Comm Part Diff Equations, 2000, 25: 737-754
doi: 10.1080/03605300008821529
|
| [9] |
Alì D, Bini D, Rionero S. Existence and relaxation limit for smooth solution to the Euler-Poisson model for semiconductors. Siam J Math Anal, 2000, 32: 572-587
doi: 10.1137/S0036141099355174
|
| [10] |
Alì G, Jüngel A. Global smooth solutions to the multi-dimensional hydrodynamic model for two-carrier plasmas. J Diff Equations, 2003, 190: 663-685
doi: 10.1016/S0022-0396(02)00157-2
|
| [11] |
Gasser I, Levermore C D, Markowich P, Shmeiser C. The initial time layer problem and the quasi-neutral limit in the semiconductor drift-diffusion model. European J Appl Math, 2001, 12: 497-512
doi: 10.1017/S0956792501004533
|
| [12] |
Guo Y, Strauss W. Stability of semiconductor states with insulating and contact boundary conditions. Arch Rat Mech and Anal, 2006, 179: 1-30
doi: 10.1007/s00205-005-0369-2
|
| [13] |
Hsiao L, Li F C, Wang S. Coupled quasi-neutral and inviscid limit of the Vlasov-Poisson-Fokker-Planck system. Commun Pure Appl Anal, 2008, 7: 579-589
|
| [14] |
Jüngel A. Peng Y J. Ahierarchy of hydrodynamic models for plasmas: Quasi-neutral limits in the drift-diffusion equations. Asymptot Anal, 2001, 28: 49-73
|
| [15] |
Roubicek T. Nonlinear Partial Differential Equations with Applications. Basel: Birkhauser Verlag, 2005
|
| [16] |
Suzuki M. Asymptotic stability of stationary solutions to the Euler-Poisson equations arising in plasma physics. Kinet Relat Models, 2011, 4: 569-588
doi: 10.3934/krm.2011.4.569
|
| [17] |
Temam R. Navier-Stokes Equations Theory and Numerical Analysis. New York: North-Holland, 1977
|
| [18] |
Wang S. Quasi-neutral limit of Euler-Poisson system with and without viscosity. Comm Part Diff Equations, 2004, 29: 419-456
doi: 10.1081/PDE-120030403
|
| [19] |
Wang S. Quasi-neutral limit of the multi-dimensional drift-diffusion-Poisson model for semiconductor with pn-junctions. Math Models Methods Appl Sci, 2006, 16: 737-757
|
| [20] |
Hsiao L, Wang S. Quasi-neureal limit of a time dependent drift-diffusion-Poisson model for p-n junction semiconductor devices. J Diff Eqns, 2006, 225: 411-439
doi: 10.1016/j.jde.2006.01.022
|
),He Jinman1,2(