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Analysis on the initial-boundary value problem of a full bipolar hydrodynamic model for semiconductors
1. | School of Mathematics and Statistics, Northeast Normal University, Changchun, MO 130024, China, China |
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] |
K. Bløtekjær, Transport equations for electrons in two-valley semiconductors, IEEE Trans. Electron Devices, 17 (1970), 38-47.
doi: 10.1109/T-ED.1970.16921. |
[3] |
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. |
[4] |
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. |
[5] |
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. |
[6] |
D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Reprint of the 1998 edition, Springer-Verlag, Berlin, 2001. |
[7] |
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. |
[8] |
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. |
[9] |
F. Huang and Y. Li, Large time behavior and quasineutral limit of solutions to a bipolar hydrodynamic model with large data and vacuum, Discrete Contin. Dyn. Syst., 24 (2009), 455-470.
doi: 10.3934/dcds.2009.24.455. |
[10] |
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. |
[11] |
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. |
[12] |
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. |
[13] |
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. |
[14] |
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. |
[15] |
S. Kawashima, Y. Nikkuni and S. Nishibata, The initial value problem for hyperbolic-elliptic coupled systems and applications to radiation hydrodynamics, in Analysis of systems of conservation laws, Chapman & Hall/CRC, Monogr. Surv. Pure Appl. Math., 99, (1999), 87-127. |
[16] |
S. Kawashima, Y. Nikkuni and S. Nishibata, Large-time behavior of solutions to hyperbolic-elliptic coupled systems, Arch. Rational Mech. Anal., 170 (2003), 297-329.
doi: 10.1007/s00205-003-0273-6. |
[17] |
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. |
[18] |
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. |
[19] |
Y. Li, Global existence and asymptotic behavior of smooth solutions to a bipolar Euler-Poisson equation in a bound domain, Z. Angew. Math. Phys., 64 (2013), 1125-1144.
doi: 10.1007/s00033-012-0269-x. |
[20] |
W. McLean, Strongly Elliptic Systems and Boundary Integral Equations, Cambridge University Press, Cambridge, 2000. |
[21] |
P. A. Markowich, C. A. Ringhofer and C. Schmeiser, Semiconductor Equations, Springer-Verlag, Vienna, 1990.
doi: 10.1007/978-3-7091-6961-2. |
[22] |
M. Mei, B. Rubino and R. Sampalmieri, Asymptotic behavior of solutions to the bipolar hydrodynamic model of semiconductors in bounded domain, Kinetic and Related Models, 5 (2012), 537-550.
doi: 10.3934/krm.2012.5.537. |
[23] |
R. Natalini, The bipolar hydrodynamic model for semiconductors and the drift-diffusion equation, J. Math. Anal. Appl., 198 (1996), 262-281.
doi: 10.1006/jmaa.1996.0081. |
[24] |
S. Nishibata and M. Suzuki, Asymptotic stability of a stationary solution to a hydrodynamic model of semiconductors, Osaka J. Math., 44 (2007), 639-665. |
[25] |
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. |
[26] |
S. Schochet, The compressible Euler equations in a bounded domain: Existence of solutions and the incompressible limit, Commun. Math. Phys., 104 (1986), 49-75.
doi: 10.1007/BF01210792. |
[27] |
R. Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, $2^{nd}$ edition, Springer-Verlag, New York, 1997.
doi: 10.1007/978-1-4612-0645-3. |
[28] |
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. |
[29] |
J. T. Wloka, B. Rowley and B. Lawruk, Boundary Value Problems for Elliptic Systems, Cambridge University Press, Cambridge, 1995.
doi: 10.1017/CBO9780511662850. |
[30] |
E. Zeidler, Nonlinear Functional Analysis and Its Applications. II/A. Linear Monotone Operators, Springer-Verlag, New York, 1990.
doi: 10.1007/978-1-4612-0985-0. |
[31] |
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. |
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] |
K. Bløtekjær, Transport equations for electrons in two-valley semiconductors, IEEE Trans. Electron Devices, 17 (1970), 38-47.
doi: 10.1109/T-ED.1970.16921. |
[3] |
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. |
[4] |
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. |
[5] |
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. |
[6] |
D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Reprint of the 1998 edition, Springer-Verlag, Berlin, 2001. |
[7] |
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. |
[8] |
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. |
[9] |
F. Huang and Y. Li, Large time behavior and quasineutral limit of solutions to a bipolar hydrodynamic model with large data and vacuum, Discrete Contin. Dyn. Syst., 24 (2009), 455-470.
doi: 10.3934/dcds.2009.24.455. |
[10] |
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. |
[11] |
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. |
[12] |
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. |
[13] |
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. |
[14] |
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. |
[15] |
S. Kawashima, Y. Nikkuni and S. Nishibata, The initial value problem for hyperbolic-elliptic coupled systems and applications to radiation hydrodynamics, in Analysis of systems of conservation laws, Chapman & Hall/CRC, Monogr. Surv. Pure Appl. Math., 99, (1999), 87-127. |
[16] |
S. Kawashima, Y. Nikkuni and S. Nishibata, Large-time behavior of solutions to hyperbolic-elliptic coupled systems, Arch. Rational Mech. Anal., 170 (2003), 297-329.
doi: 10.1007/s00205-003-0273-6. |
[17] |
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. |
[18] |
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. |
[19] |
Y. Li, Global existence and asymptotic behavior of smooth solutions to a bipolar Euler-Poisson equation in a bound domain, Z. Angew. Math. Phys., 64 (2013), 1125-1144.
doi: 10.1007/s00033-012-0269-x. |
[20] |
W. McLean, Strongly Elliptic Systems and Boundary Integral Equations, Cambridge University Press, Cambridge, 2000. |
[21] |
P. A. Markowich, C. A. Ringhofer and C. Schmeiser, Semiconductor Equations, Springer-Verlag, Vienna, 1990.
doi: 10.1007/978-3-7091-6961-2. |
[22] |
M. Mei, B. Rubino and R. Sampalmieri, Asymptotic behavior of solutions to the bipolar hydrodynamic model of semiconductors in bounded domain, Kinetic and Related Models, 5 (2012), 537-550.
doi: 10.3934/krm.2012.5.537. |
[23] |
R. Natalini, The bipolar hydrodynamic model for semiconductors and the drift-diffusion equation, J. Math. Anal. Appl., 198 (1996), 262-281.
doi: 10.1006/jmaa.1996.0081. |
[24] |
S. Nishibata and M. Suzuki, Asymptotic stability of a stationary solution to a hydrodynamic model of semiconductors, Osaka J. Math., 44 (2007), 639-665. |
[25] |
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. |
[26] |
S. Schochet, The compressible Euler equations in a bounded domain: Existence of solutions and the incompressible limit, Commun. Math. Phys., 104 (1986), 49-75.
doi: 10.1007/BF01210792. |
[27] |
R. Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, $2^{nd}$ edition, Springer-Verlag, New York, 1997.
doi: 10.1007/978-1-4612-0645-3. |
[28] |
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. |
[29] |
J. T. Wloka, B. Rowley and B. Lawruk, Boundary Value Problems for Elliptic Systems, Cambridge University Press, Cambridge, 1995.
doi: 10.1017/CBO9780511662850. |
[30] |
E. Zeidler, Nonlinear Functional Analysis and Its Applications. II/A. Linear Monotone Operators, Springer-Verlag, New York, 1990.
doi: 10.1007/978-1-4612-0985-0. |
[31] |
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. |
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