Discrete approximation of the Poisson-Vlasov system
Author:
Jack Schaeffer
Journal:
Quart. Appl. Math. 45 (1987), 59-73
MSC:
Primary 35Q20; Secondary 65M99
DOI:
https://doi.org/10.1090/qam/885168
MathSciNet review:
885168
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Abstract: Solutions of the Poisson-Vlasov system of equations that have spherical symmetry are considered. A numerical scheme which exploits the symmetry is proposed and is shown to converge in a pointwise sense. Prior convergence results due to Neunzert conclude convergence in only a weak topology although they require no symmetry.
- C. Bardos and P. Degond, Global existence for the Vlasov-Poisson equation in $3$ space variables with small initial data, Ann. Inst. H. Poincaré Anal. Non Linéaire 2 (1985), no. 2, 101–118 (English, with French summary). MR 794002
- Jürgen Batt, Global symmetric solutions of the initial value problem of stellar dynamics, J. Differential Equations 25 (1977), no. 3, 342–364. MR 487082, DOI https://doi.org/10.1016/0022-0396%2877%2990049-3
E. Horst, On the classical solutions of the initial value problem for the unmodified nonlinear Vlasov equation, Parts 1 and 2, Math. Methods Appl. Sci. 3, 229–248 (1981); 4, 19–32 (1982)
- Rudolf Kurth, Das Anfangswertproblem der Stellardynamik, Z. Astrophys. 30 (1952), 213–229 (German). MR 61940
H. Neunzert, Mathematical investigations on particle-in-cell methods, Fluid Dynamics Trans. 9, 229–254 (1978)
- Stephen Wollman, The spherically symmetric Vlasov-Poisson system, J. Differential Equations 35 (1980), no. 1, 30–35. MR 556789, DOI https://doi.org/10.1016/0022-0396%2880%2990046-7
C. Bardos and P. Degond, Global existence for the Vlasov-Poisson equation in 3 space variables with small initial data. Preprint.
J. Batt, Global symmetric solutions of the initial value problem of stellar dynamics, J. Differential Equations 25, 342–364 (1977)
E. Horst, On the classical solutions of the initial value problem for the unmodified nonlinear Vlasov equation, Parts 1 and 2, Math. Methods Appl. Sci. 3, 229–248 (1981); 4, 19–32 (1982)
R. Kurth, Das Anfangswertproblem der Stellardynamik, Z. Astrophys. 30, 213–229 (1952)
H. Neunzert, Mathematical investigations on particle-in-cell methods, Fluid Dynamics Trans. 9, 229–254 (1978)
S. Wollman, The spherically symmetric Vlasov-Poisson system, J. Differential Equations 35, 30–35 (1980)
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Article copyright:
© Copyright 1987
American Mathematical Society
