Download PDF - Growth and accretion of mass in an astrophysical model, IIAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Growth and accretion of mass in an astrophysical model, II

Authors 1, 1

Affiliations

  1. Mathematical Institute, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Abstract

Radially symmetric solutions of a nonlocal Fokker-Planck equation describing the evolution of self-attracting particles in a bounded container are studied. Conditions ensuring either global-in-time existence of solutions or their finite time blow up are given.

Keywords

ENG
radial solutions, global and blowing up solutions, nonlinear parabolic equation

Bibliography

  1. P. Biler, Growth and accretion of mass in an astrophysical model, Appl. Math. (Warsaw) 23 (1995), 179-189.
  2. P. Biler, Local and global solutions of a nonlinear nonlocal parabolic problem, in: Proc. of the Banach Center minisemester 'Nonlinear Analysis and Applications', to appear.
  3. P. Biler, Existence and nonexistence of solutions for a model of gravitational interaction of particles, III, Colloq. Math. 68 (1995), 229-339.
  4. P. Biler, D. Hilhorst and T. Nadzieja, Existence and nonexistence of solutions for a model of gravitational interaction of particles, II, ibid. 67 (1994), 297-308.
  5. P. Biler and T. Nadzieja, Existence and nonexistence of solutions for a model of gravitational interaction of particles, I, ibid. 66 (1994), 319-334.
  6. A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, N.J., 1964.
  7. W. Jäger and S. Luckhaus, On explosions of solutions to a system of partial differential equations modelling chemotaxis, Trans. Amer. Math. Soc. 329 (1992), 819-824.
  8. S. Karlin and H. M. Taylor, A Second Course in Stochastic Processes, Academic Press, New York, 1981.
  9. O. A. Ladyženskaja [O. A. Ladyzhenskaya], V. A. Solonnikov and N. N. Ural'ceva [N. N. Ural'tseva], Linear and Quasilinear Equations of Parabolic Type, Amer. Math. Soc., Providence, R.I., 1988.
  10. T. Nadzieja, A model of a radially symmetric cloud of self-attracting particles, Appl. Math. (Warsaw) 23 (1995), 169-178.
  11. G. Wolansky, On steady distributions of self-attracting clusters under friction and fluctuations, Arch. Rational Mech. Anal. 119 (1992), 355-391.
  12. G. Wolansky, On the evolution of self-interacting clusters and applications to semilinear equations with exponential nonlinearity, J. Anal. Math. 59 (1992), 251-272.
Applicationes Mathematicae
1995-1996/23/3
Export to PBN, Opens in new tab
Pages:
351-361
Main language of publication
English
Received
1995-01-24
Published
1995
Exact and natural sciences