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Stability of the stationary solution of the cauchy problem to a semiconductor full hydrodynamic model with recombination-generation rate
1. | School of Mathematics and Statistics, Northeast Normal University, Changchun, MO 130024 |
References:
[1] |
G. Ali, D. Bini and S. Rionero, Global existence and relaxation limit for smooth solutions to the Euler-Poisson model for semiconductors, SIAM J. Math. Anal., 32 (2000), 572-587.
doi: 10.1137/S0036141099355174. |
[2] |
G. Alì and A. Jüngel, Global smooth solutions to the multi-dimensional hydrodynamic model for two-carrier plasmas, J. Differential Equations, 190 (2003), 663-685.
doi: 10.1016/S0022-0396(02)00157-2. |
[3] |
S. Dimitrijev, Principles of Semiconductor Devices, Oxford University Press, 2nd edition, Oxford, 2011. |
[4] |
P. Degond and P. Markowich, On a one-dimensional steady-state hydrodynamic model, Appl. Math. Lett., 3 (1990), 25-29.
doi: 10.1016/0893-9659(90)90130-4. |
[5] |
D. Donatelli, M. Mei, B. Rubino and R. Sampalmieri, Asymptotic behavior of solutions to Euler-Poisson equations for bipolar hydrodynamic model of semiconductors, J. Differential Equations, 255 (2013), 3150-3184.
doi: 10.1016/j.jde.2013.07.027. |
[6] |
W. Fang and K. Ito, Energy estimates for a one-dimensional hydrodynamic model of semiconductors, Appl. Math. Lett., 9 (1996), 65-70.
doi: 10.1016/0893-9659(96)00053-5. |
[7] |
W. Fang and K. Ito, Weak solutions to a one-dimensional hydrodynamic model of two carrier types for semiconductors, Nonlinear Anal., 28 (1997), 947-963.
doi: 10.1016/0362-546X(95)00189-3. |
[8] |
I. Gasser, L. Hsiao and H. Li, Large time behavior of solutions of the bipolar hydrodynamical model for semiconductors, J. Differential Equations, 192 (2003), 326-359.
doi: 10.1016/S0022-0396(03)00122-0. |
[9] |
Y. Guo and W. Strauss, Stability of semiconductor states with insulating and contact boundary conditions, Arch. Rational Mech. Anal., 179 (2006), 1-30.
doi: 10.1007/s00205-005-0369-2. |
[10] |
D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics, 840. Springer-Verlag, Berlin-New York, 1981. |
[11] |
L. Hsiao, S. Jiang and P. Zhang, Global existence and exponential stability of smooth solutions to a full hydrodynamic model to semiconductors, Monatsh. Math., 136 (2002), 269-285.
doi: 10.1007/s00605-002-0485-0. |
[12] |
F. Huang, M. Mei and Y. Wang, Large time behavior of solutions to n-dimensional bipolar hydrodynamic model for semiconductors, SIAM J. Math. Anal., 43 (2011), 1595-1630.
doi: 10.1137/100810228. |
[13] |
F. Huang, M. Mei, Y. Wang and H. Yu, Asymptotic convergence to stationary waves for unipolar hydrodynamic model of semiconductors, SIAM J. Math. Anal., 43 (2011), 411-429.
doi: 10.1137/100793025. |
[14] |
F. Huang, M. Mei, Y. Wang and H. Yu, Asymptotic convergence to planar stationary waves for multi-dimensional unipolar hydrodynamic model of semiconductors, J. Differential Equations, 251 (2011), 1305-1331.
doi: 10.1016/j.jde.2011.04.007. |
[15] |
F. Huang, M. Mei, Y. Wang and T. Yang, Long-time behavior of solutions to the bipolar hydrodynamic model of semiconductors with boundary effect, SIAM J. Math. Anal., 44 (2012), 1134-1164.
doi: 10.1137/110831647. |
[16] |
L. Hsiao and S. Wang, Asymptotic behavior of global smooth solutions to the full 1D hydrodynamic model for semiconductors, Math.Models Methods Appl.Sci., 12 (2002), 777-796.
doi: 10.1142/S0218202502001891. |
[17] |
L. Hsiao and K. Zhang, The global weak solution and relaxation limits of the initial-boundary value problem to the bipolar hydrodynamic model for semiconductors, Math. Models Methods Appl.Sci., 10 (2000), 1333-1361.
doi: 10.1142/S0218202500000653. |
[18] |
H. Hu and K. Zhang, Analysis on the initial-boundary value problem of a full bipolar hydrodynamic model for semiconductors, Discrete Contin.Dyn.Syst.Ser.B, 19 (2014), 1601-1626.
doi: 10.3934/dcdsb.2014.19.1601. |
[19] |
A. Jüngel, Quasi-Hydrodynamic Semiconductor Equations, Progress in Nonlinear Differential Equations and their Applications, Birkhäuser Verlag, Besel-Boston-Berlin, 2001.
doi: 10.1007/978-3-0348-8334-4. |
[20] |
H. Li, P. Markowich and M. Mei, Asymptotic behaviour of solutions of the hydrodynamic model of semiconductors, Proc. Roy. Soc. Edinburgh Sect. A, 132 (2002), 359-378.
doi: 10.1017/S0308210500001670. |
[21] |
T. Luo, R. Natalini and Z. Xin, Large time behavior of the solutions to a hydrodynamic model for semiconductors, SIAM J. Appl. Math., 59 (1999), 810-830.
doi: 10.1137/S0036139996312168. |
[22] |
P. A. Markowich, C. A. Ringhofer and C. Schmeiser, Semiconductor Equations, Springer-Verlag, Vienna, 1990.
doi: 10.1007/978-3-7091-6961-2. |
[23] |
A. Majda, Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables, Applied Mathematical Sciences, 53. Springer-Verlag, New York, 1984.
doi: 10.1007/978-1-4612-1116-7. |
[24] |
A. Matsumura and T. Nishida, The initial value problem for the equations of motion of viscous and heat-conductive gases, J. Math. Kyoto Univ., 20 (1980), 67-104. |
[25] |
N. J. Mauser, Y. Qiu and K. Zhang, Global existence and asymptotic limits of weak solutions of the bipolar hydrodynamic model for semiconductors, Monatsh. Math., 140 (2003), 285-313.
doi: 10.1007/s00605-002-0543-7. |
[26] |
M. Mei and Y. Wang, Stability of stationary waves for full Euler-Poisson system in multi-dimensional space, Commun. Pure Appl. Anal., 11 (2012), 1775-1807.
doi: 10.3934/cpaa.2012.11.1775. |
[27] |
R. Natalini, The bipolar hydrodynamic model for semiconductors and the drift-diffusion equations, J. Math. Anal. Appl., 198 (1996), 262-281.
doi: 10.1006/jmaa.1996.0081. |
[28] |
S. Nishibata and M. Suzuki, Asymptotic stability of a stationary solution to a hydrodynamic model of semiconductors, Osaka J. Math., 44 (2007), 639-665. |
[29] |
S. Nishibata and M. Suzuki, Asymptotic stability of a stationary solution to a thermal hydrodynamic model for semiconductors, Arch. Rational Mech. Anal., 192 (2009), 187-215.
doi: 10.1007/s00205-008-0129-1. |
[30] |
Y. Peng and J. Xu, Global well-posedness of the hydrodynamic model for two-carrier plasmas, J. Differential Equations, 255 (2013), 3447-3471.
doi: 10.1016/j.jde.2013.07.045. |
[31] |
N. Tsuge, Existence and uniqueness of stationary solutions to a one-dimensional bipolar hydrodynamic model of semiconductors, Nonlinear Anal., 73 (2010), 779-787.
doi: 10.1016/j.na.2010.04.015. |
[32] |
D. Wang, Global solutions to the Euler-Poisson equations of two-carrier types in one dimension, Z. Angew. Math. Phys., 48 (1997), 680-693.
doi: 10.1007/s000330050056. |
[33] |
K. Zhang, On the initial-boundary value problem for the bipolar hydrodynamic model for semiconductors, J. Differential Equations, 171 (2001), 251-293.
doi: 10.1006/jdeq.2000.3850. |
[34] |
C. Zhu and H. Hattori, Asymptotic behavior of the solution to a nonisentropic hydrodynamic model of semiconductors, J. Differential Equations, 144 (1998), 353-389.
doi: 10.1006/jdeq.1997.3381. |
[35] |
C. Zhu and H. Hattori, Stability of steady state solutions for an isentropic hydrodynamic model of semiconductors of two species, J. Differential Equations, 166 (2000), 1-32.
doi: 10.1006/jdeq.2000.3799. |
show all references
References:
[1] |
G. Ali, D. Bini and S. Rionero, Global existence and relaxation limit for smooth solutions to the Euler-Poisson model for semiconductors, SIAM J. Math. Anal., 32 (2000), 572-587.
doi: 10.1137/S0036141099355174. |
[2] |
G. Alì and A. Jüngel, Global smooth solutions to the multi-dimensional hydrodynamic model for two-carrier plasmas, J. Differential Equations, 190 (2003), 663-685.
doi: 10.1016/S0022-0396(02)00157-2. |
[3] |
S. Dimitrijev, Principles of Semiconductor Devices, Oxford University Press, 2nd edition, Oxford, 2011. |
[4] |
P. Degond and P. Markowich, On a one-dimensional steady-state hydrodynamic model, Appl. Math. Lett., 3 (1990), 25-29.
doi: 10.1016/0893-9659(90)90130-4. |
[5] |
D. Donatelli, M. Mei, B. Rubino and R. Sampalmieri, Asymptotic behavior of solutions to Euler-Poisson equations for bipolar hydrodynamic model of semiconductors, J. Differential Equations, 255 (2013), 3150-3184.
doi: 10.1016/j.jde.2013.07.027. |
[6] |
W. Fang and K. Ito, Energy estimates for a one-dimensional hydrodynamic model of semiconductors, Appl. Math. Lett., 9 (1996), 65-70.
doi: 10.1016/0893-9659(96)00053-5. |
[7] |
W. Fang and K. Ito, Weak solutions to a one-dimensional hydrodynamic model of two carrier types for semiconductors, Nonlinear Anal., 28 (1997), 947-963.
doi: 10.1016/0362-546X(95)00189-3. |
[8] |
I. Gasser, L. Hsiao and H. Li, Large time behavior of solutions of the bipolar hydrodynamical model for semiconductors, J. Differential Equations, 192 (2003), 326-359.
doi: 10.1016/S0022-0396(03)00122-0. |
[9] |
Y. Guo and W. Strauss, Stability of semiconductor states with insulating and contact boundary conditions, Arch. Rational Mech. Anal., 179 (2006), 1-30.
doi: 10.1007/s00205-005-0369-2. |
[10] |
D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics, 840. Springer-Verlag, Berlin-New York, 1981. |
[11] |
L. Hsiao, S. Jiang and P. Zhang, Global existence and exponential stability of smooth solutions to a full hydrodynamic model to semiconductors, Monatsh. Math., 136 (2002), 269-285.
doi: 10.1007/s00605-002-0485-0. |
[12] |
F. Huang, M. Mei and Y. Wang, Large time behavior of solutions to n-dimensional bipolar hydrodynamic model for semiconductors, SIAM J. Math. Anal., 43 (2011), 1595-1630.
doi: 10.1137/100810228. |
[13] |
F. Huang, M. Mei, Y. Wang and H. Yu, Asymptotic convergence to stationary waves for unipolar hydrodynamic model of semiconductors, SIAM J. Math. Anal., 43 (2011), 411-429.
doi: 10.1137/100793025. |
[14] |
F. Huang, M. Mei, Y. Wang and H. Yu, Asymptotic convergence to planar stationary waves for multi-dimensional unipolar hydrodynamic model of semiconductors, J. Differential Equations, 251 (2011), 1305-1331.
doi: 10.1016/j.jde.2011.04.007. |
[15] |
F. Huang, M. Mei, Y. Wang and T. Yang, Long-time behavior of solutions to the bipolar hydrodynamic model of semiconductors with boundary effect, SIAM J. Math. Anal., 44 (2012), 1134-1164.
doi: 10.1137/110831647. |
[16] |
L. Hsiao and S. Wang, Asymptotic behavior of global smooth solutions to the full 1D hydrodynamic model for semiconductors, Math.Models Methods Appl.Sci., 12 (2002), 777-796.
doi: 10.1142/S0218202502001891. |
[17] |
L. Hsiao and K. Zhang, The global weak solution and relaxation limits of the initial-boundary value problem to the bipolar hydrodynamic model for semiconductors, Math. Models Methods Appl.Sci., 10 (2000), 1333-1361.
doi: 10.1142/S0218202500000653. |
[18] |
H. Hu and K. Zhang, Analysis on the initial-boundary value problem of a full bipolar hydrodynamic model for semiconductors, Discrete Contin.Dyn.Syst.Ser.B, 19 (2014), 1601-1626.
doi: 10.3934/dcdsb.2014.19.1601. |
[19] |
A. Jüngel, Quasi-Hydrodynamic Semiconductor Equations, Progress in Nonlinear Differential Equations and their Applications, Birkhäuser Verlag, Besel-Boston-Berlin, 2001.
doi: 10.1007/978-3-0348-8334-4. |
[20] |
H. Li, P. Markowich and M. Mei, Asymptotic behaviour of solutions of the hydrodynamic model of semiconductors, Proc. Roy. Soc. Edinburgh Sect. A, 132 (2002), 359-378.
doi: 10.1017/S0308210500001670. |
[21] |
T. Luo, R. Natalini and Z. Xin, Large time behavior of the solutions to a hydrodynamic model for semiconductors, SIAM J. Appl. Math., 59 (1999), 810-830.
doi: 10.1137/S0036139996312168. |
[22] |
P. A. Markowich, C. A. Ringhofer and C. Schmeiser, Semiconductor Equations, Springer-Verlag, Vienna, 1990.
doi: 10.1007/978-3-7091-6961-2. |
[23] |
A. Majda, Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables, Applied Mathematical Sciences, 53. Springer-Verlag, New York, 1984.
doi: 10.1007/978-1-4612-1116-7. |
[24] |
A. Matsumura and T. Nishida, The initial value problem for the equations of motion of viscous and heat-conductive gases, J. Math. Kyoto Univ., 20 (1980), 67-104. |
[25] |
N. J. Mauser, Y. Qiu and K. Zhang, Global existence and asymptotic limits of weak solutions of the bipolar hydrodynamic model for semiconductors, Monatsh. Math., 140 (2003), 285-313.
doi: 10.1007/s00605-002-0543-7. |
[26] |
M. Mei and Y. Wang, Stability of stationary waves for full Euler-Poisson system in multi-dimensional space, Commun. Pure Appl. Anal., 11 (2012), 1775-1807.
doi: 10.3934/cpaa.2012.11.1775. |
[27] |
R. Natalini, The bipolar hydrodynamic model for semiconductors and the drift-diffusion equations, J. Math. Anal. Appl., 198 (1996), 262-281.
doi: 10.1006/jmaa.1996.0081. |
[28] |
S. Nishibata and M. Suzuki, Asymptotic stability of a stationary solution to a hydrodynamic model of semiconductors, Osaka J. Math., 44 (2007), 639-665. |
[29] |
S. Nishibata and M. Suzuki, Asymptotic stability of a stationary solution to a thermal hydrodynamic model for semiconductors, Arch. Rational Mech. Anal., 192 (2009), 187-215.
doi: 10.1007/s00205-008-0129-1. |
[30] |
Y. Peng and J. Xu, Global well-posedness of the hydrodynamic model for two-carrier plasmas, J. Differential Equations, 255 (2013), 3447-3471.
doi: 10.1016/j.jde.2013.07.045. |
[31] |
N. Tsuge, Existence and uniqueness of stationary solutions to a one-dimensional bipolar hydrodynamic model of semiconductors, Nonlinear Anal., 73 (2010), 779-787.
doi: 10.1016/j.na.2010.04.015. |
[32] |
D. Wang, Global solutions to the Euler-Poisson equations of two-carrier types in one dimension, Z. Angew. Math. Phys., 48 (1997), 680-693.
doi: 10.1007/s000330050056. |
[33] |
K. Zhang, On the initial-boundary value problem for the bipolar hydrodynamic model for semiconductors, J. Differential Equations, 171 (2001), 251-293.
doi: 10.1006/jdeq.2000.3850. |
[34] |
C. Zhu and H. Hattori, Asymptotic behavior of the solution to a nonisentropic hydrodynamic model of semiconductors, J. Differential Equations, 144 (1998), 353-389.
doi: 10.1006/jdeq.1997.3381. |
[35] |
C. Zhu and H. Hattori, Stability of steady state solutions for an isentropic hydrodynamic model of semiconductors of two species, J. Differential Equations, 166 (2000), 1-32.
doi: 10.1006/jdeq.2000.3799. |
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