- Previous Article
- KRM Home
- This Issue
-
Next Article
Growth estimates and uniform decay for a collisionless plasma
Asymptotic stability of stationary solutions to the Euler-Poisson equations arising in plasma physics
1. | Research Institute of Nonlinear Partial Differential Equations, Organization for University Research Initiatives, Waseda University, Tokyo 169-8555, Japan |
References:
[1] |
A. Ambroso, Stability for solutions of a stationary Euler-Poisson problem, Math. Models Methods Appl. Sci., 16 (2006), 1817-1837.
doi: 10.1142/S0218202506001728. |
[2] |
A. Ambroso, F. Méhats and P.-A. Raviart, On singular perturbation problems for the nonlinear Poisson equation, Asympt. Anal., 25 (2001), 39-91. |
[3] |
F. F. Chen, "Introduction to Plasma Physics and Controlled Fusion,'' 2nd edition, Springer, 1984. |
[4] |
S. Cordier, P. Degond, P. Markowich and C. Schmeiser, Travelling wave analysis of an isothermal Euler-Poisson model, Ann. Fac. Sci. Toulouse Math., 5 (1996), 599-643. |
[5] |
S. Cordier, P. Degond, P. Markowich and C. Schmeiser, Travelling wave analysis and jump relations for Euler-Poisson model in the quasineutral limit, Asymptotic Anal., 11 (1995), 209-240. |
[6] |
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. |
[7] |
S.-H. Ha and M. Slemrod, Global existence of plasma ion-sheaths and their dynamics, Comm. Math. Phys., 238 (2003), 149-186. |
[8] |
Y. Guo and W. Strauss, Stability of semiconductor states with insulating and contact boundary conditions, Arch. Ration. Mech. Anal., 179 (2006), 1-30.
doi: 10.1007/s00205-005-0369-2. |
[9] |
T. Kato, Linear evolution equations of "hyperbolic'' type, J. Math. Soc. Japan., 25 (1973), 648-666.
doi: 10.2969/jmsj/02540648. |
[10] |
S. Kawashima and A. Matsumura, Asymptotic stability of traveling wave solutions of systems for one-dimensional gas motion, Comm. Math. Phys., 101 (1985), 97-127.
doi: 10.1007/BF01212358. |
[11] |
S. Kawashima, Y. Nikkuni and S. Nishibata, Large-time behavior of solutions to hyperbolic-elliptic coupled systems, Arch. Ration. Mech. Anal., 170 (2003), 297-329.
doi: 10.1007/s00205-003-0273-6. |
[12] |
M. A. Lieberman and A. J. Lichtenberg, "Principles of Plasma Discharges and Materials Processing,'' 2nd edition, Wiley-Interscience, 2005.
doi: 10.1002/0471724254. |
[13] |
T. Nakamura, S. Nishibata and T. Yuge, Convergence rate of solutions toward stationary solutions to the compressible Navier-Stokes equation in a half line, J. Differ. Equ., 241 (2007), 94-111.
doi: 10.1016/j.jde.2007.06.016. |
[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, Asymptotic stability of a stationary solution to a thermal hydrodynamic model for semiconductors, Arch. Ration. Mech. Anal., 192 (2009), 187-215.
doi: 10.1007/s00205-008-0129-1. |
[16] |
S. Nishibata and M. Suzuki, Relaxation limit and initial layer to hydrodynamic models for semiconductors, J. Differ. Equ., 249 (2010), 1385-1409.
doi: 10.1016/j.jde.2010.06.008. |
[17] |
M. Nishikawa, Convergence rate to the traveling wave for viscous conservation laws, Funkcial. Ekvac., 41 (1998), 107-132. |
[18] |
M. Slemrod, The radio-frequency driven plasma sheath: asymptotics and analysis, SIAM J. Appl. Math., 63 (2003), 1737-1763.
doi: 10.1137/S0036139902411831. |
[19] |
N. Sternberg and V. A. Godyak, Solving the mathematical model of the electrode sheath in symmetrically driven rf discharges, J. Comput. Phys., 111 (1994), 347-353.
doi: 10.1006/jcph.1994.1068. |
[20] |
Y.-J. Peng and Y.-G. Wang, Boundary layers and quasi-neutral limit in steady state Euler-Poisson equations for potential flows, Nonlinearity, 17 (2004), 835-849.
doi: 10.1088/0951-7715/17/3/006. |
[21] |
K.-U. Riemann, The Bohm criterion and sheath formation. Initial value problems, J. Phys. D: Appl. Phys., 24 (1991), 493-518.
doi: 10.1088/0022-3727/24/4/001. |
[22] |
M.-H. Vignal, A boundary layer problem for an asymptotic preserving scheme in the quasi-neutral limit for the Euler-Poisson system, SIAM J. Appl. Math., 70 (2010), 1761-1787.
doi: 10.1137/070703272. |
show all references
References:
[1] |
A. Ambroso, Stability for solutions of a stationary Euler-Poisson problem, Math. Models Methods Appl. Sci., 16 (2006), 1817-1837.
doi: 10.1142/S0218202506001728. |
[2] |
A. Ambroso, F. Méhats and P.-A. Raviart, On singular perturbation problems for the nonlinear Poisson equation, Asympt. Anal., 25 (2001), 39-91. |
[3] |
F. F. Chen, "Introduction to Plasma Physics and Controlled Fusion,'' 2nd edition, Springer, 1984. |
[4] |
S. Cordier, P. Degond, P. Markowich and C. Schmeiser, Travelling wave analysis of an isothermal Euler-Poisson model, Ann. Fac. Sci. Toulouse Math., 5 (1996), 599-643. |
[5] |
S. Cordier, P. Degond, P. Markowich and C. Schmeiser, Travelling wave analysis and jump relations for Euler-Poisson model in the quasineutral limit, Asymptotic Anal., 11 (1995), 209-240. |
[6] |
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. |
[7] |
S.-H. Ha and M. Slemrod, Global existence of plasma ion-sheaths and their dynamics, Comm. Math. Phys., 238 (2003), 149-186. |
[8] |
Y. Guo and W. Strauss, Stability of semiconductor states with insulating and contact boundary conditions, Arch. Ration. Mech. Anal., 179 (2006), 1-30.
doi: 10.1007/s00205-005-0369-2. |
[9] |
T. Kato, Linear evolution equations of "hyperbolic'' type, J. Math. Soc. Japan., 25 (1973), 648-666.
doi: 10.2969/jmsj/02540648. |
[10] |
S. Kawashima and A. Matsumura, Asymptotic stability of traveling wave solutions of systems for one-dimensional gas motion, Comm. Math. Phys., 101 (1985), 97-127.
doi: 10.1007/BF01212358. |
[11] |
S. Kawashima, Y. Nikkuni and S. Nishibata, Large-time behavior of solutions to hyperbolic-elliptic coupled systems, Arch. Ration. Mech. Anal., 170 (2003), 297-329.
doi: 10.1007/s00205-003-0273-6. |
[12] |
M. A. Lieberman and A. J. Lichtenberg, "Principles of Plasma Discharges and Materials Processing,'' 2nd edition, Wiley-Interscience, 2005.
doi: 10.1002/0471724254. |
[13] |
T. Nakamura, S. Nishibata and T. Yuge, Convergence rate of solutions toward stationary solutions to the compressible Navier-Stokes equation in a half line, J. Differ. Equ., 241 (2007), 94-111.
doi: 10.1016/j.jde.2007.06.016. |
[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, Asymptotic stability of a stationary solution to a thermal hydrodynamic model for semiconductors, Arch. Ration. Mech. Anal., 192 (2009), 187-215.
doi: 10.1007/s00205-008-0129-1. |
[16] |
S. Nishibata and M. Suzuki, Relaxation limit and initial layer to hydrodynamic models for semiconductors, J. Differ. Equ., 249 (2010), 1385-1409.
doi: 10.1016/j.jde.2010.06.008. |
[17] |
M. Nishikawa, Convergence rate to the traveling wave for viscous conservation laws, Funkcial. Ekvac., 41 (1998), 107-132. |
[18] |
M. Slemrod, The radio-frequency driven plasma sheath: asymptotics and analysis, SIAM J. Appl. Math., 63 (2003), 1737-1763.
doi: 10.1137/S0036139902411831. |
[19] |
N. Sternberg and V. A. Godyak, Solving the mathematical model of the electrode sheath in symmetrically driven rf discharges, J. Comput. Phys., 111 (1994), 347-353.
doi: 10.1006/jcph.1994.1068. |
[20] |
Y.-J. Peng and Y.-G. Wang, Boundary layers and quasi-neutral limit in steady state Euler-Poisson equations for potential flows, Nonlinearity, 17 (2004), 835-849.
doi: 10.1088/0951-7715/17/3/006. |
[21] |
K.-U. Riemann, The Bohm criterion and sheath formation. Initial value problems, J. Phys. D: Appl. Phys., 24 (1991), 493-518.
doi: 10.1088/0022-3727/24/4/001. |
[22] |
M.-H. Vignal, A boundary layer problem for an asymptotic preserving scheme in the quasi-neutral limit for the Euler-Poisson system, SIAM J. Appl. Math., 70 (2010), 1761-1787.
doi: 10.1137/070703272. |
[1] |
Sun-Ho Choi. Weighted energy method and long wave short wave decomposition on the linearized compressible Navier-Stokes equation. Networks and Heterogeneous Media, 2013, 8 (2) : 465-479. doi: 10.3934/nhm.2013.8.465 |
[2] |
Hiroshi Takeda. Large time behavior of solutions for a nonlinear damped wave equation. Communications on Pure and Applied Analysis, 2016, 15 (1) : 41-55. doi: 10.3934/cpaa.2016.15.41 |
[3] |
Jinyan Fan, Jianyu Pan. On the convergence rate of the inexact Levenberg-Marquardt method. Journal of Industrial and Management Optimization, 2011, 7 (1) : 199-210. doi: 10.3934/jimo.2011.7.199 |
[4] |
Yves Bourgault, Damien Broizat, Pierre-Emmanuel Jabin. Convergence rate for the method of moments with linear closure relations. Kinetic and Related Models, 2015, 8 (1) : 1-27. doi: 10.3934/krm.2015.8.1 |
[5] |
Mingshang Hu, Xiaojuan Li, Xinpeng Li. Convergence rate of Peng’s law of large numbers under sublinear expectations. Probability, Uncertainty and Quantitative Risk, 2021, 6 (3) : 261-266. doi: 10.3934/puqr.2021013 |
[6] |
Philippe Laurençot, Christoph Walker. The fragmentation equation with size diffusion: Small and large size behavior of stationary solutions. Kinetic and Related Models, 2021, 14 (6) : 961-980. doi: 10.3934/krm.2021032 |
[7] |
Emre Esentürk, Juan Velazquez. Large time behavior of exchange-driven growth. Discrete and Continuous Dynamical Systems, 2021, 41 (2) : 747-775. doi: 10.3934/dcds.2020299 |
[8] |
Geonho Lee, Sangdong Kim, Young-Sam Kwon. Large time behavior for the full compressible magnetohydrodynamic flows. Communications on Pure and Applied Analysis, 2012, 11 (3) : 959-971. doi: 10.3934/cpaa.2012.11.959 |
[9] |
Carlos E. Kenig. The method of energy channels for nonlinear wave equations. Discrete and Continuous Dynamical Systems, 2019, 39 (12) : 6979-6993. doi: 10.3934/dcds.2019240 |
[10] |
Haibo Cui, Haiyan Yin. Convergence rate of solutions toward stationary solutions to the isentropic micropolar fluid model in a half line. Discrete and Continuous Dynamical Systems - B, 2021, 26 (6) : 2899-2920. doi: 10.3934/dcdsb.2020210 |
[11] |
Tohru Nakamura, Shinya Nishibata, Naoto Usami. Convergence rate of solutions towards the stationary solutions to symmetric hyperbolic-parabolic systems in half space. Kinetic and Related Models, 2018, 11 (4) : 757-793. doi: 10.3934/krm.2018031 |
[12] |
Shan Ma, Chunyou Sun. Long-time behavior for a class of weighted equations with degeneracy. Discrete and Continuous Dynamical Systems, 2020, 40 (3) : 1889-1902. doi: 10.3934/dcds.2020098 |
[13] |
Roman Czapla, Vladimir V. Mityushev. A criterion of collective behavior of bacteria. Mathematical Biosciences & Engineering, 2017, 14 (1) : 277-287. doi: 10.3934/mbe.2017018 |
[14] |
Yaonan Ma, Li-Zhi Liao. The Glowinski–Le Tallec splitting method revisited: A general convergence and convergence rate analysis. Journal of Industrial and Management Optimization, 2021, 17 (4) : 1681-1711. doi: 10.3934/jimo.2020040 |
[15] |
Martin Burger, Marco Di Francesco. Large time behavior of nonlocal aggregation models with nonlinear diffusion. Networks and Heterogeneous Media, 2008, 3 (4) : 749-785. doi: 10.3934/nhm.2008.3.749 |
[16] |
Dongfen Bian, Boling Guo. Global existence and large time behavior of solutions to the electric-magnetohydrodynamic equations. Kinetic and Related Models, 2013, 6 (3) : 481-503. doi: 10.3934/krm.2013.6.481 |
[17] |
Kin Ming Hui, Soojung Kim. Asymptotic large time behavior of singular solutions of the fast diffusion equation. Discrete and Continuous Dynamical Systems, 2017, 37 (11) : 5943-5977. doi: 10.3934/dcds.2017258 |
[18] |
Cong He, Hongjun Yu. Large time behavior of the solution to the Landau Equation with specular reflective boundary condition. Kinetic and Related Models, 2013, 6 (3) : 601-623. doi: 10.3934/krm.2013.6.601 |
[19] |
Jie Zhao. Large time behavior of solution to quasilinear chemotaxis system with logistic source. Discrete and Continuous Dynamical Systems, 2020, 40 (3) : 1737-1755. doi: 10.3934/dcds.2020091 |
[20] |
Joana Terra, Noemi Wolanski. Large time behavior for a nonlocal diffusion equation with absorption and bounded initial data. Discrete and Continuous Dynamical Systems, 2011, 31 (2) : 581-605. doi: 10.3934/dcds.2011.31.581 |
2020 Impact Factor: 1.432
Tools
Metrics
Other articles
by authors
[Back to Top]