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Asymptotic stability of steady state solutions for the relativistic Euler-Poisson equations
1. | Department of Mathematics, Capital Normal University, Beijing 100048, China |
2. | School of Mathematics and Statistics, Northeast Normal University, Changchun, MO 130024 |
References:
[1] |
P. Degond and P. A. Markowich, On a one-dimensional steady-state hydrodynamic model for semiconductors, Appl. Math. Lett., 3 (1990), 25-29.
doi: 10.1016/0893-9659(90)90130-4. |
[2] |
I. Gamba, Stationary transonic solutions of a one-dimensional hydrodynamic model for semiconductor, Comm. Partial Differential Equations, 17 (1992), 553-577.
doi: 10.1080/03605309208820853. |
[3] |
J. P. Goedbloed, R. Keppens and S. Poedts, Advanced Magnetohydrodynamics: With Applications to Laboratory and Astrophysical Plasmas, Cambridge University Press, 2010.
doi: 10.1017/CBO9781139195560. |
[4] |
Y. Guo and W. Strauss, Stability of semiconductor states with insulating and contact boundary, Arch. Ration. Mech. Anal., 179 (2006), 1-30.
doi: 10.1007/s00205-005-0369-2. |
[5] |
L. Hsiao and K. J. Zhang, The relaxation of the hydrodynamic model for semiconductors to the drift-diffusion equations, J. Differential Equations, 165 (2000), 315-354.
doi: 10.1006/jdeq.2000.3780. |
[6] |
F. M. 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. |
[7] |
H. L. Li, P. A. 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. |
[8] |
T. Luo, R. Natalini and Z. Xin, Large time behavior of the solutions to a hydrodynamic model for semiconductors, SIAM J. Math. Anal., 59 (1999), 810-830.
doi: 10.1137/S0036139996312168. |
[9] |
La-Su. Mai, J. Y. Li and K. J. Zhang, On the steady state relativistic Euler-Poisson equations, Acta. Appl. Math., 125 (2013), 135-157.
doi: 10.1007/s10440-012-9784-1. |
[10] |
A. Majda, Compressible Fluid Flow and System of Conservation Laws in Several Space Variables, (Appl. Math. Sci. 53), Springer, 1984. |
[11] |
P. A. Marcati and R. Natalini, Weak solutions to a hydrodynamic model for semiconductors and relaxation to the drift-diffusion equation, Arch. Ration. Mech. Analysis., 129 (1995), 129-145.
doi: 10.1007/BF00379918. |
[12] |
P. Marcati and R. Natalini, Weak solutions to a hydrodynamic model for semiconductors: The Cauchy problem, Proc. Roy. Soc. Edinburgh Sect. A, 125 (1995), 115-131.
doi: 10.1017/S030821050003078X. |
[13] |
P. A. Markowich, The Stationary Semiconductor Device Equations, Computational Microelectronics, Springer-Verlag, Vienna, 1986. |
[14] |
S. Nishibata and M. Suzuki, Asymptotic stability of a stationary solution to a hydrodynamic model of semiconductors, Osaka J. Math., 44 (2007), 639-665. |
[15] |
S. Nishibata and M. Suzuki, Relaxation limit and initial layer to hydrodynamic models for semiconductors, J. Differential Equations, 249 (2010), 1385-1409.
doi: 10.1016/j.jde.2010.06.008. |
[16] |
V. Pant, On I. Symmetry Breaking Under Perturbations and II. Relativistic Fluid Dynamics, Ph. D. Thesis, University of Michigan, 1996. |
[17] |
Y. J. Peng, Asymptotic limits of one-dimensional hydrodynamic models for plasmas and semiconductors, Chinese Ann. Math. Ser. B, 23 (2002), 25-36.
doi: 10.1142/S0252959902000043. |
[18] |
F. Poupaud, M. Rascle and J. P. Vila, Global solutions to the isothermal Euler-Poisson system with arbitrarily large data, J. Differential Equations, 123 (1995), 93-121.
doi: 10.1006/jdeq.1995.1158. |
[19] |
S. Schochet, The compressible Euler equations in a bounded domain: Existence of solutions and the incompressible limit, Comm. Math. Phys., 104 (1986), 49-75.
doi: 10.1007/BF01210792. |
[20] |
B, Zhang, On a local existence theorem for a simplified one-dimensional hydrodynamic model for semiconductor devices, SIAM J. Math. Anal., 25 (1994), 941-947.
doi: 10.1137/S0036141092224595. |
show all references
References:
[1] |
P. Degond and P. A. Markowich, On a one-dimensional steady-state hydrodynamic model for semiconductors, Appl. Math. Lett., 3 (1990), 25-29.
doi: 10.1016/0893-9659(90)90130-4. |
[2] |
I. Gamba, Stationary transonic solutions of a one-dimensional hydrodynamic model for semiconductor, Comm. Partial Differential Equations, 17 (1992), 553-577.
doi: 10.1080/03605309208820853. |
[3] |
J. P. Goedbloed, R. Keppens and S. Poedts, Advanced Magnetohydrodynamics: With Applications to Laboratory and Astrophysical Plasmas, Cambridge University Press, 2010.
doi: 10.1017/CBO9781139195560. |
[4] |
Y. Guo and W. Strauss, Stability of semiconductor states with insulating and contact boundary, Arch. Ration. Mech. Anal., 179 (2006), 1-30.
doi: 10.1007/s00205-005-0369-2. |
[5] |
L. Hsiao and K. J. Zhang, The relaxation of the hydrodynamic model for semiconductors to the drift-diffusion equations, J. Differential Equations, 165 (2000), 315-354.
doi: 10.1006/jdeq.2000.3780. |
[6] |
F. M. 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. |
[7] |
H. L. Li, P. A. 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. |
[8] |
T. Luo, R. Natalini and Z. Xin, Large time behavior of the solutions to a hydrodynamic model for semiconductors, SIAM J. Math. Anal., 59 (1999), 810-830.
doi: 10.1137/S0036139996312168. |
[9] |
La-Su. Mai, J. Y. Li and K. J. Zhang, On the steady state relativistic Euler-Poisson equations, Acta. Appl. Math., 125 (2013), 135-157.
doi: 10.1007/s10440-012-9784-1. |
[10] |
A. Majda, Compressible Fluid Flow and System of Conservation Laws in Several Space Variables, (Appl. Math. Sci. 53), Springer, 1984. |
[11] |
P. A. Marcati and R. Natalini, Weak solutions to a hydrodynamic model for semiconductors and relaxation to the drift-diffusion equation, Arch. Ration. Mech. Analysis., 129 (1995), 129-145.
doi: 10.1007/BF00379918. |
[12] |
P. Marcati and R. Natalini, Weak solutions to a hydrodynamic model for semiconductors: The Cauchy problem, Proc. Roy. Soc. Edinburgh Sect. A, 125 (1995), 115-131.
doi: 10.1017/S030821050003078X. |
[13] |
P. A. Markowich, The Stationary Semiconductor Device Equations, Computational Microelectronics, Springer-Verlag, Vienna, 1986. |
[14] |
S. Nishibata and M. Suzuki, Asymptotic stability of a stationary solution to a hydrodynamic model of semiconductors, Osaka J. Math., 44 (2007), 639-665. |
[15] |
S. Nishibata and M. Suzuki, Relaxation limit and initial layer to hydrodynamic models for semiconductors, J. Differential Equations, 249 (2010), 1385-1409.
doi: 10.1016/j.jde.2010.06.008. |
[16] |
V. Pant, On I. Symmetry Breaking Under Perturbations and II. Relativistic Fluid Dynamics, Ph. D. Thesis, University of Michigan, 1996. |
[17] |
Y. J. Peng, Asymptotic limits of one-dimensional hydrodynamic models for plasmas and semiconductors, Chinese Ann. Math. Ser. B, 23 (2002), 25-36.
doi: 10.1142/S0252959902000043. |
[18] |
F. Poupaud, M. Rascle and J. P. Vila, Global solutions to the isothermal Euler-Poisson system with arbitrarily large data, J. Differential Equations, 123 (1995), 93-121.
doi: 10.1006/jdeq.1995.1158. |
[19] |
S. Schochet, The compressible Euler equations in a bounded domain: Existence of solutions and the incompressible limit, Comm. Math. Phys., 104 (1986), 49-75.
doi: 10.1007/BF01210792. |
[20] |
B, Zhang, On a local existence theorem for a simplified one-dimensional hydrodynamic model for semiconductor devices, SIAM J. Math. Anal., 25 (1994), 941-947.
doi: 10.1137/S0036141092224595. |
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