References
- Donatelli D, Mei M, Rubino B, et al. Asymptotic behavior of solutions to the Cauchy problem of Euler–Poisson equations. J Diff Equ. 2013;255:3150–3184. doi: 10.1016/j.jde.2013.07.027
- Gasser I, Hsiao L, Li H. Large time behavior of solutions of the bipolar hydrodynamical model for semiconductors. J Diff Equ. 2003;192(2):326–359. doi: 10.1016/S0022-0396(03)00122-0
- Hu H, Mei M, Zhang K. Relaxation limit in bipolar semiconductor hydrodynamic model with non-constant doping profile. J Math Anal Appl. 2017;448(2):1175–1203. doi: 10.1016/j.jmaa.2016.11.043
- Hu H, Zhang K. Stability of the stationary solution of the Cauchy problem to a semiconductor full hydrodynamic model with recombination-generation rate. Kinet Relat Mod. 2015;8(1):117–151. doi: 10.3934/krm.2015.8.117
- Huang F, Mei M, Wang Y. Large-time behavior of solutions to n-dimensional bipolar hydrodynamical model of semiconductors. SIAM J Math Anal. 2011;43(4):1595–1630. doi: 10.1137/100810228
- Huang F, Mei M, Wang Y, et al. Long-time behavior of solutions for bipolar hydrodynamic model of semiconductors with boundary effects. SIAM J Math Anal. 2012;44:1134–1164. doi: 10.1137/110831647
- Sampalmieri R, Rubino B, Mei M. Asymptotic behavior of solutions to the bipolar hydrodynamic model of semiconductors in bounded domain. Kinet Relat Mod. 2012;5:537–550. doi: 10.3934/krm.2012.5.537
- Peng Y, Xu J. Global well-posedness of the hydrodynamic model for two-carrier plasmas. J Diff Equ. 2013;255(10):3447–3471. doi: 10.1016/j.jde.2013.07.045
- Tsuge N. Existence and uniqueness of stationary solutions to a one-dimensional bipolar hydrodynamic model of semiconductors. Nonlinear Anal. 2010;73(3):779–787. doi: 10.1016/j.na.2010.04.015
- Zhang G, Li HL, Zhang K. Semiclassical and relaxation limits of bipolar quantum hydrodynamic model for semiconductors. J Diff Equ. 2008;245:1433–1453. doi: 10.1016/j.jde.2008.06.019
- Degond P, Markowich PA. A steady state potential flow model for semiconductors. Ann Mat Pura Appl. 1993;165(4):87–98. doi: 10.1007/BF01765842
- Li H, Markowich PA, Mei M. Asymptotic behaviour of solutions of the hydrodynamic model of semiconductors. Proc Roy Soc Edinb. 2002;132A:359–378. doi: 10.1017/S0308210500001670
- Nishibata S, Suzuki M. Asymptotic stability of a stationary solution to a hydrodynamic model of semiconductors. Osaka J Math. 2007;44(3):639–665.
- Guo Y, Strauss W. Stability of semiconductor states with insulating and contact boundary conditions. Arch Ration Mech Anal. 2006;179(1):1–30. doi: 10.1007/s00205-005-0369-2
- Luo T, Natalini R, Xin Z. Large time behavior of the solutions to a hydrodynamic model for semiconductors. SIAM J Appl Math. 1999;59(3):810–830.
- Huang F, Mei M, Wang Y, et al. Asymptotic convergence to stationary waves for unipolar hydrodynamic model of semiconductors. SIAM J Math Anal. 2011;43(1):411–429. doi: 10.1137/100793025
- Mock MS. An initial value problem from semiconductor device theory. SIAM J Math Anal. 1974;5:597–612. doi: 10.1137/0505061
- Mock MS. Asymptotic behavior of solutions of transport equations for semiconductor devices. J Math Anal Appl. 1975;49:215–225. doi: 10.1016/0022-247X(75)90172-9
- Adams R, Fournier J. Sobolev spaces. Amsterdam: Elsevier/Academic Press; 2003.
- Gilbarg D, Trudinger NS. Elliptic partial differential equations of second order. Berlin: Springer-Verlag; 2001.