New stationary distributions of the Vlasov-Maxwell-Fokker-Planck’s system. (English) Zbl 1238.82025
Summary: In this paper we investigate the nonlinear Vlasov-Maxwell-Fokker-Planck (VMFP) system. We propose new families of distributions for the stationary VMFP equation, which is reduced to certain systems of nonlinear elliptic equations depending on arbitrary parameters. We consider the cases when these elliptic systems allow the reduction to the nonlinear PDEs of fourth order, or to the well-known Liouville equation.
MSC:
| 82C31 | Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics |
| 35J60 | Nonlinear elliptic equations |
| 82C05 | Classical dynamic and nonequilibrium statistical mechanics (general) |
| 35Q84 | Fokker-Planck equations |
Keywords:
Vlasov-Maxwell-Fokker-Planck equation; steady state solution; nonlinear elliptic system; nonlinear PDE of the fourth order; Liouville equationReferences:
| [1] | Dressler, K., Math. Methods Appl. Sci., 12, 471 (1990) · Zbl 0703.35170 |
| [2] | Glassey, R.; Schaeffer, J.; Zheng, Y., J. Appl. Math. Anal. Appl., 202, 3, 1058 (1996), (18) · Zbl 0867.35026 |
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