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Stationary spherically symmetric models in stellar dynamics. (English) Zbl 0605.70008
The initial value problem of stellar dynamics - Vlasov equation, Poisson’s equation, density distribution - is investigated for the case of stationary, spherically symmetric solutions. Precise statements about the distribution function $$\phi$$ are given; a factorization theorem for $$\phi$$ is introduced. Some examples are given.

##### MSC:
 70F15 Celestial mechanics 70Sxx Classical field theories 85A05 Galactic and stellar dynamics 35A08 Fundamental solutions to PDEs
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##### References:
 [1] Batt, J., Global symmetric solutions of the initial value problem of stellar dynamics. J. Differential Equations 25, 342-364 (1977). · Zbl 0366.35020 · doi:10.1016/0022-0396(77)90049-3 [2] Batt, J., Recent developments in the mathematical investigation of the initial value problem of stellar dynamics and plasma physics. Ann. Nuclear Energy 7, 213-217 (1980). · doi:10.1016/0306-4549(80)90067-5 [3] Camm, G. L., Self-gravitating star systems II. Monthly Notices Royal Astronomical Society 112, 155-176 (1952). · Zbl 0049.44203 [4] Chandrasekhar, S., An introduction to the study of stellar structure. Chicago: Dover Publications 1957. · Zbl 0079.23901 [5] Eddington, A. S., The dynamical equilibrium of the stellar system. Astronom. Nachr., Jubiläumsnummer, 9-10 (1921). [6] Emden, R., Gaskugeln. Leipzig und Berlin: Teubner 1907. [7] Fowler, R. H., The solutions of Emden’s and similar differential equations. Monthly Notices Royal Astronomical Society 91, 63-91 (1930). · JFM 56.0389.02 [8] Fowler, R. H., Further studies of Emden’s and similar differential equations. Quarterly J. Math. Oxford Ser. 2, 259-288 (1931). · Zbl 0003.23502 · doi:10.1093/qmath/os-2.1.259 [9] Hopf, E., On Emden’s differential equation. Monthly Notices Royal Astronomical Society 91, 653-663 (1931). · Zbl 0002.10301 [10] Horst, E., On the classical solutions of the initial value problem for the unmodified non-linear Vlasov equation I. Math. Meth. Appl. Sci. 3, 229-248 (1981). · Zbl 0463.35071 · doi:10.1002/mma.1670030117 [11] Horst, E., On the classical solutions of the initial value problem for the unmodified non-linear Vlasov equation II. Math. Meth. Appl. Sci. 4, 19-32 (1982). · Zbl 0485.35079 · doi:10.1002/mma.1670040104 [12] Jeans, J. H., On the theory of star-streaming and the structure of the universe. Monthly Notices Royal Astronomical Society 76, 70-84 (1915). [13] Jeans, J. H., Problems of cosmogony and stellar dynamics. Cambridge, University Press 1919. · JFM 47.0848.01 [14] Kurth, R., General theory of spherical self-gravitating star systems in a steady state. Astronom. Nachr. 282, 97-106 (1955). · Zbl 0065.45502 · doi:10.1002/asna.19552820302 [15] Kurth, R., Stellar orbits in globular clusters. Astronom. Nachr. 282, 241-246 (1955). · doi:10.1002/asna.19552820602 [16] Kurth, R., Introduction to the mechanics of stellar systems. London: Pergamon Press 1957. · Zbl 0084.23805 [17] Kurth, R., A global particular solution to the initial value problem of stellar dynamics. Quarterly Appl. Math. 36, 325-329 (1978). · Zbl 0391.70015 [18] Sansone, G., Sulle soluzione di Emden dell’equazione di Fowler. Rend. Mat. Roma 1, 163-176 (1940). [19] Shiveshwarkar, S. W., Remarks on some theorems in the dynamics of a steady stellar system. Monthly Notices Royal Astronomical Society 96, 749-758 (1936). · Zbl 0014.42003 [20] Walter, W., Entire solutions of the differential equation ?u=f(u). J. Austral. Math. Soc. (Series A) 30, 366-368 (1981). · Zbl 0468.35041 · doi:10.1017/S1446788700017249
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