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A kinetic reaction model: Decay to equilibrium and macroscopic limit
Asymptotic stability of a boundary layer to the Euler--Poisson equations for a multicomponent plasma
1. | Department of Computer Science and Engineering, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya, 466-8555, 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] |
D. Bohm, Minimum ionic kinetic energy for a stable sheath, in The characteristics of electrical discharges in magnetic fields (eds. A. Guthrie and R.K.Wakerling), McGraw-Hill, New York, (1949), 77-86. |
[4] |
F. F. Chen, Introduction to Plasma Physics and Controlled Fusion, $2^{nd}$ edition, Springer, 1984. |
[5] |
S.-H. Ha and M. Slemrod, Global existence of plasma ion-sheaths and their dynamics, Comm. Math. Phys., 238 (2003), 149-186.
doi: 10.1007/s00220-003-0871-z. |
[6] |
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. |
[7] |
I. Langmuir, The interaction of electron and positive ion space charges in cathode sheaths, Phys. Rev., 33 (1929), 954-989.
doi: 10.1103/PhysRev.33.954. |
[8] |
M. A. Lieberman and A. J. Lichtenberg, Principles of Plasma Discharges and Materials Processing, $2^{nd}$ edition, Wiley-Interscience, 2005.
doi: 10.1002/0471724254. |
[9] |
S. Nishibata, M. Ohnawa and M. Suzuki, Asymptotic stability of boundary layers to the Euler-Poisson equations arising in plasma physics, SIAM J. Math. Anal., 44 (2012), 761-790.
doi: 10.1137/110835657. |
[10] |
M. Nishikawa, Convergence rate to the traveling wave for viscous conservation laws, Funkcial. Ekvac., 41 (1998), 107-132. |
[11] |
K.-U. Riemann, The Bohm criterion and sheath formation. Initial value problems, J. Phys. D: Appl. Phys., 24 (1991), 493-518. |
[12] |
K.-U. Riemann, The Bohm criterion and boundary conditions for a multicomponent system, IEEE Trans. Plasma Sci., 23 (1995), 709-716.
doi: 10.1109/27.467993. |
[13] |
M. Suzuki, Asymptotic stability of stationary solutions to the Euler-Poisson equations arising in plasma physics, Kinet. Relat. Models, 4 (2011), 569-588.
doi: 10.3934/krm.2011.4.569. |
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] |
D. Bohm, Minimum ionic kinetic energy for a stable sheath, in The characteristics of electrical discharges in magnetic fields (eds. A. Guthrie and R.K.Wakerling), McGraw-Hill, New York, (1949), 77-86. |
[4] |
F. F. Chen, Introduction to Plasma Physics and Controlled Fusion, $2^{nd}$ edition, Springer, 1984. |
[5] |
S.-H. Ha and M. Slemrod, Global existence of plasma ion-sheaths and their dynamics, Comm. Math. Phys., 238 (2003), 149-186.
doi: 10.1007/s00220-003-0871-z. |
[6] |
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. |
[7] |
I. Langmuir, The interaction of electron and positive ion space charges in cathode sheaths, Phys. Rev., 33 (1929), 954-989.
doi: 10.1103/PhysRev.33.954. |
[8] |
M. A. Lieberman and A. J. Lichtenberg, Principles of Plasma Discharges and Materials Processing, $2^{nd}$ edition, Wiley-Interscience, 2005.
doi: 10.1002/0471724254. |
[9] |
S. Nishibata, M. Ohnawa and M. Suzuki, Asymptotic stability of boundary layers to the Euler-Poisson equations arising in plasma physics, SIAM J. Math. Anal., 44 (2012), 761-790.
doi: 10.1137/110835657. |
[10] |
M. Nishikawa, Convergence rate to the traveling wave for viscous conservation laws, Funkcial. Ekvac., 41 (1998), 107-132. |
[11] |
K.-U. Riemann, The Bohm criterion and sheath formation. Initial value problems, J. Phys. D: Appl. Phys., 24 (1991), 493-518. |
[12] |
K.-U. Riemann, The Bohm criterion and boundary conditions for a multicomponent system, IEEE Trans. Plasma Sci., 23 (1995), 709-716.
doi: 10.1109/27.467993. |
[13] |
M. Suzuki, Asymptotic stability of stationary solutions to the Euler-Poisson equations arising in plasma physics, Kinet. Relat. Models, 4 (2011), 569-588.
doi: 10.3934/krm.2011.4.569. |
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