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On a class of elliptic operators with unbounded diffusion coefficients
A one-dimensional kinetic model of plasma dynamics with a transport field
1. | Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019, United States |
2. | Department of Applied Mathematics and Statistics, Colorado School of Mines, Golden, CO 80002, United States |
References:
[1] |
F. Bouchut, F. Golse and C. Pallard, Classical solutions and the Glassey-Strauss theorem for the 3D Vlasov-Maxwell system, Arch. Ration. Mech. Anal., 170 (2003), 1-15.
doi: 10.1007/s00205-003-0265-6. |
[2] |
D. Brewer and S. Pankavich, Computational Methods for a One-dimensional Plasma Model with a Transport Field, SIAM Undergraduate Research Online, 4 (2011), 81-104. |
[3] |
R. J. DiPerna and P. L. Lions, Global weak solutions of Vlasov-Maxwell systems, Comm. Pure Appl. Math., 42 (1989), 729-757.
doi: 10.1002/cpa.3160420603. |
[4] |
P. Gerard and C. Pallard, A mean-field toy model for resonant transport, Kinet. Relat. Models, 3 (2010), 299-309.
doi: 10.3934/krm.2010.3.299. |
[5] |
R. T. Glassey, The Cauchy Problem in Kinetic Theory, Society for Industrial and Applied Mathematics (SIAM): Philadelphia, PA, 1996.
doi: 10.1137/1.9781611971477. |
[6] |
R. T. Glassey and J. Schaeffer, On the "one and one-half dimensional'' relativistic Vlasov-Maxwell system, Math. Methods Appl. Sci., 13 (1990), 169-179.
doi: 10.1002/mma.1670130207. |
[7] |
R. T. Glassey and W. A. Strauss, Singularity formation in a collisionless plasma could occur only at high velocities, Arch. Rational Mech. Anal., 92 (1986), 59-90.
doi: 10.1007/BF00250732. |
[8] |
S. Klainerman and G. Staffilani, A new approach to study the Vlasov-Maxwell system, Commun. Pure Appl. Anal., 1 (2002), 103-125. |
[9] |
M. Kunzinger, G. Rein, R. Steinbauer and G. Teschl, On classical solutions of the relativistic Vlasov-Klein-Gordon system, Electron. J. Differential Equations (electronic - 17 pp.), 1 (2005), 17pp. |
[10] |
S. Pankavich, Global existence for the Vlasov-Poisson system with steady spatial asymptotics, Comm. Partial Differential Equations, 31 (2006), 349-370.
doi: 10.1080/03605300500358004. |
[11] |
S. Pankavich, Local existence for the one-dimensional Vlasov-Poisson system with infinite mass, Math. Methods Appl. Sci., 30 (2007), 529-548.
doi: 10.1002/mma.796. |
[12] |
N. G. van Kampen and B. U. Felderhof, Theoretical Methods in Plasma Physics, Wiley: New York, NY, 1967. |
show all references
References:
[1] |
F. Bouchut, F. Golse and C. Pallard, Classical solutions and the Glassey-Strauss theorem for the 3D Vlasov-Maxwell system, Arch. Ration. Mech. Anal., 170 (2003), 1-15.
doi: 10.1007/s00205-003-0265-6. |
[2] |
D. Brewer and S. Pankavich, Computational Methods for a One-dimensional Plasma Model with a Transport Field, SIAM Undergraduate Research Online, 4 (2011), 81-104. |
[3] |
R. J. DiPerna and P. L. Lions, Global weak solutions of Vlasov-Maxwell systems, Comm. Pure Appl. Math., 42 (1989), 729-757.
doi: 10.1002/cpa.3160420603. |
[4] |
P. Gerard and C. Pallard, A mean-field toy model for resonant transport, Kinet. Relat. Models, 3 (2010), 299-309.
doi: 10.3934/krm.2010.3.299. |
[5] |
R. T. Glassey, The Cauchy Problem in Kinetic Theory, Society for Industrial and Applied Mathematics (SIAM): Philadelphia, PA, 1996.
doi: 10.1137/1.9781611971477. |
[6] |
R. T. Glassey and J. Schaeffer, On the "one and one-half dimensional'' relativistic Vlasov-Maxwell system, Math. Methods Appl. Sci., 13 (1990), 169-179.
doi: 10.1002/mma.1670130207. |
[7] |
R. T. Glassey and W. A. Strauss, Singularity formation in a collisionless plasma could occur only at high velocities, Arch. Rational Mech. Anal., 92 (1986), 59-90.
doi: 10.1007/BF00250732. |
[8] |
S. Klainerman and G. Staffilani, A new approach to study the Vlasov-Maxwell system, Commun. Pure Appl. Anal., 1 (2002), 103-125. |
[9] |
M. Kunzinger, G. Rein, R. Steinbauer and G. Teschl, On classical solutions of the relativistic Vlasov-Klein-Gordon system, Electron. J. Differential Equations (electronic - 17 pp.), 1 (2005), 17pp. |
[10] |
S. Pankavich, Global existence for the Vlasov-Poisson system with steady spatial asymptotics, Comm. Partial Differential Equations, 31 (2006), 349-370.
doi: 10.1080/03605300500358004. |
[11] |
S. Pankavich, Local existence for the one-dimensional Vlasov-Poisson system with infinite mass, Math. Methods Appl. Sci., 30 (2007), 529-548.
doi: 10.1002/mma.796. |
[12] |
N. G. van Kampen and B. U. Felderhof, Theoretical Methods in Plasma Physics, Wiley: New York, NY, 1967. |
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