Time decay for solutions to one-dimensional two component plasma equations
Authors:
Robert Glassey, Jack Schaeffer and Stephen Pankavich
Journal:
Quart. Appl. Math. 68 (2010), 135-141
MSC (2000):
Primary 35L60, 35Q99, 82C21, 82C22, 82D10.
DOI:
https://doi.org/10.1090/S0033-569X-09-01143-4
Published electronically:
October 28, 2009
MathSciNet review:
2598885
Full-text PDF Free Access
References |
Similar Articles |
Additional Information
References
- Jürgen Batt, Markus Kunze, and Gerhard Rein, On the asymptotic behaviour of a one-dimensional monocharged plasma and a rescaling method, Adv. Differential Equations 3 (1998), no. 2, 271–292. MR 1750415
- Burgan, J.R.; Feix, M.R.; Fijalkow, E.; Munier, A., Self-similar and asymptotic solutions for a one-dimensional Vlasov beam. J. Plasma Physics 1983, 29:139–142.
- L. Desvillettes and J. Dolbeault, On long time asymptotics of the Vlasov-Poisson-Boltzmann equation, Comm. Partial Differential Equations 16 (1991), no. 2-3, 451–489. MR 1104107, DOI https://doi.org/10.1080/03605309108820765
- Jean Dolbeault, Time-dependent rescalings and Lyapunov functionals for some kinetic and fluid models, Proceedings of the Fifth International Workshop on Mathematical Aspects of Fluid and Plasma Dynamics (Maui, HI, 1998), 2000, pp. 537–549. MR 1770442, DOI https://doi.org/10.1080/00411450008205890
- J. Dolbeault and G. Rein, Time-dependent rescalings and Lyapunov functionals for the Vlasov-Poisson and Euler-Poisson systems, and for related models of kinetic equations, fluid dynamics and quantum physics, Math. Models Methods Appl. Sci. 11 (2001), no. 3, 407–432. MR 1830948, DOI https://doi.org/10.1142/S021820250100091X
- Robert T. Glassey and Walter A. Strauss, Remarks on collisionless plasmas, Fluids and plasmas: geometry and dynamics (Boulder, Colo., 1983) Contemp. Math., vol. 28, Amer. Math. Soc., Providence, RI, 1984, pp. 269–279. MR 751989, DOI https://doi.org/10.1090/conm/028/751989
- Reinhard Illner and Gerhard Rein, Time decay of the solutions of the Vlasov-Poisson system in the plasma physical case, Math. Methods Appl. Sci. 19 (1996), no. 17, 1409–1413. MR 1414402, DOI https://doi.org/10.1002/%28SICI%291099-1476%2819961125%2919%3A17%3C1409%3A%3AAID-MMA836%3E3.3.CO%3B2-U
- P.-L. Lions and B. Perthame, Propagation of moments and regularity for the $3$-dimensional Vlasov-Poisson system, Invent. Math. 105 (1991), no. 2, 415–430 (English, with French summary). MR 1115549, DOI https://doi.org/10.1007/BF01232273
- B. Perthame, Time decay, propagation of low moments and dispersive effects for kinetic equations, Comm. Partial Differential Equations 21 (1996), no. 3-4, 659–686 (English, with English and French summaries). MR 1387464, DOI https://doi.org/10.1080/03605309608821201
- Glassey, R., Pankavich, S. and Schaeffer, J. Decay in time for a one dimensional two component plasma. Math. Methods Appl. Sci 2008, 31(18):2115–2132.
- K. Pfaffelmoser, Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data, J. Differential Equations 95 (1992), no. 2, 281–303. MR 1165424, DOI https://doi.org/10.1016/0022-0396%2892%2990033-J
- Jack Schaeffer, Large-time behavior of a one-dimensional monocharged plasma, Differential Integral Equations 20 (2007), no. 3, 277–292. MR 2293986
References
- Batt, J.; Kunze, M.; and Rein, G., On the asymptotic behavior of a one-dimensional, monocharged plasma and a rescaling method. Advances in Differential Equations 1998, 3:271–292. MR 1750415 (2001c:82077)
- Burgan, J.R.; Feix, M.R.; Fijalkow, E.; Munier, A., Self-similar and asymptotic solutions for a one-dimensional Vlasov beam. J. Plasma Physics 1983, 29:139–142.
- Desvillettes, L. and Dolbeault, J., On long time asymptotics of the Vlasov–Poisson–Boltzmann equation. Comm. Partial Differential Equations 1991, 16(2-3):451–489. MR 1104107 (92b:35153)
- Dolbeault, J. Time-dependent rescalings and Lyapunov functionals for some kinetic and fluid models. Proceedings of the Fifth International Workshop on Mathematical Aspects of Fluid and Plasma Dynamics (Maui, HI, 1998). Transport Theory Statist. Phys. 2000, 29(3-5):537–549. MR 1770442 (2001f:76063)
- Dolbeault, J. and Rein, G. Time-dependent rescalings and Lyapunov functionals for the Vlasov-Poisson and Euler-Poisson systems, and for related models of kinetic equations, fluid dynamics and quantum physics. Math. Methods Appl. Sci. 2001, 11(3):407–432. MR 1830948 (2002f:82034)
- Glassey, R. and Strauss, W., Remarks on collisionless plasmas. Contemporary Mathematics 1984, 28:269–279. MR 751989 (85m:76077)
- Illner, R. and Rein, G., Time decay of the solutions of the Vlasov-Poisson system in the plasma physical case. Math. Methods Appl. Sci. 1996, 19:1409–1413. MR 1414402 (97j:35153)
- Lions, P.L. and Perthame, B. Propogation of moments and regularity for the three dimensional Vlasov-Poisson system. Invent. Math. 1991, 105:415–430. MR 1115549 (92e:35160)
- Perthame, B. Time decay, propagation of low moments and dispersive effects for kinetic equations. Comm. Partial Differential Equations 1996, 21(3–4):659–686. MR 1387464 (97e:82042)
- Glassey, R., Pankavich, S. and Schaeffer, J. Decay in time for a one dimensional two component plasma. Math. Methods Appl. Sci 2008, 31(18):2115–2132.
- Pfaffelmoser, K., Global classical solution of the Vlassov-Poisson system in three dimensions for general initial data. J. Diff. Eq. 1992, 95(2):281–303. MR 1165424 (93d:35170)
- Schaeffer, J. Large-time behavior of a one-dimensional monocharged plasma. Diff. and Int. Equations 2007, 20(3):277–292. MR 2293986 (2007k:82141)
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC (2000):
35L60,
35Q99,
82C21,
82C22,
82D10.
Retrieve articles in all journals
with MSC (2000):
35L60,
35Q99,
82C21,
82C22,
82D10.
Additional Information
Robert Glassey
Affiliation:
Department of Mathematics, Indiana University, Bloomington, Indiana 47405
Email:
glassey@indiana.edu
Jack Schaeffer
Affiliation:
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213
Email:
js5m@andrew.cmu.edu
Stephen Pankavich
Affiliation:
Department of Mathematics, University of Texas Arlington, Arlington, Texas 76019
Email:
sdp@uta.edu
Received by editor(s):
August 6, 2008
Published electronically:
October 28, 2009
Dedicated:
Dedicated to Professor Walter Strauss on his 70th birthday
Article copyright:
© Copyright 2009
Brown University
