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1997 | 41 | 1 | 179-194
Tytuł artykułu

Selfgravitating systems in Newtonian theory - the Vlasov-Poisson system

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We give a review of results on the initial value problem for the Vlasov--Poisson system, concentrating on the main ingredients in the proof of global existence of classical solutions.
Słowa kluczowe
Rocznik
Tom
41
Numer
1
Strony
179-194
Opis fizyczny
Daty
wydano
1997
Twórcy
autor
  • Mathematisches Institut der Universität München, Theresienstr., 39, 80333 München, Germany
Bibliografia
  • [1] C. Bardos and P. Degond, Global existence for the Vlasov Poisson equation in 3 space variables with small initial data, Ann. Inst. Henri Poincaré, Analyse non linéaire 2 (1985), 101-111.
  • [2] J. Batt, Global symmetric solutions of the initial value problem of stellar dynamics, J. Differential Eqns. 25 (1977), 342-364.
  • [3] J. Batt, Asymptotic properties of spherically symmetric self-gravitating mass systems for t → ∞, Transport Theory and Statistical Mechanics 16 (1987), 763-778.
  • [4] J. Batt, W. Faltenbacher, and E. Horst, Stationary spherically symmetric models in stellar dynamics, Arch. Rational Mech. Anal. 93 (1986), 159-183 .
  • [5] J. Batt, P. Morrison, and G. Rein, Linear stability of stationary solutions of the Vlasov-Poisson system in three dimensions, Arch. Rational Mech. Anal. 130 (1995), 163-182.
  • [6] J. Batt and G. Rein, A rigorous stability result for the Vlasov-Poisson system in three dimensions, Anal. di Mat. Pura ed Appl. 164 (1993), 133-154.
  • [7] F. Bouchut, Existence and uniqueness of a global smooth solution for the Vlasov-Poisson-Fokker-Planck system in three dimensions, J. Functional Analysis 111 (1993), 239-258.
  • [8] K. Ganguly and H. Victory, On the convergence of particle methods for multidimensional Vlasov-Poisson systems, SIAM J. Numer. Anal. 26 (1989), 249-288
  • [9] R. Glassey and J. Schaeffer, On symmetric solutions of the relativistic Vlasov-Poisson system, Commun. Math. Phys. 101 (1985), 459-473.
  • [10] Y. Guo and W. Strauss, Nonlinear instability of double-humped equilibria, Ann. Inst. Henri Poincaré, Analyse non linéaire 12 (1995), 339-352 .
  • [11] Y. Guo and W. Strauss, Instability of periodic BGK equilibria, Commun. Pure and Appl. Math. XLVIII (1995), 861-894.
  • [12] E. Horst, On the classical solutions of the initial value problem for the unmodified non-linear Vlasov equation II, Math. Meth. in the Appl. Sci. 4 (1982), 19-32.
  • [13] E. Horst, On the asymptotic growth of the solutions of the Vlasov-Poisson system, Math. Meth. in the Appl. Sci. 16 (1993), 75-85.
  • [14] R. Illner and G. Rein, Time decay of the solutions of the Vlasov-Poisson system in the plasma physical case, Math. Meth. in the Appl. Sci. 19 (1996), 1409-1413.
  • [15] P.-L. Lions and B. Perthame, Propagation of moments and regularity for the 3-dimensional Vlasov-Poisson system, Invent. math. 105 (1991), 415-430.
  • [16] K. Pfaffelmoser, Globale klassische Lösungen des dreidimensionalen Vlasov-Poisson-Systems, Dissertation, München 1989 .
  • [17] K. Pfaffelmoser, Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data, J. Differential Eqns. 95 (1992), 281-303.
  • [18] M. Reed and B. Simon, Methods of Modern Mathematical Physics II, Academic Press, New York, 1975.
  • [19] G. Rein, Generic global solutions of the relativistic Vlasov-Maxwell system of plasma physics, Commun. Math. Phys. 135 (1990), 41-78.
  • [20] G. Rein, Nonlinear stability for the Vlasov-Poisson system--the energy-Casimir method, Math. Meth. in the Appl. Sci. 17 (1994), 1129-1140.
  • [21] G. Rein, Growth estimates for the solutions of the Vlasov-Poisson system in the plasma physics case, Math. Nachrichten, to appear.
  • [22] G. Rein, Nonlinear stability of homogeneous models in Newtonian cosmology, Arch. Rational Mech. Anal., to appear.
  • [23] G. Rein and A. Rendall, Global existence of classical solutions to the Vlasov-Poisson system in a three-dimensional, cosmological setting, Arch. Rational Mech. Anal. 126 (1994), 183-201.
  • [24] J. Schaeffer, Global existence of smooth solutions to the Vlasov-Poisson system in three dimensions, Commun. Part. Diff. Eqns. 16 (1991), 1313-1335.
  • [25] J. Schaeffer, Global existence of smooth solutions to the Vlasov-Poisson system in three dimensions (`The Good, the Bad, and the Ugly'), unpublished manuscript.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv41z1p179bwm
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