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

ArticleOriginal scientific text

Title

Growth and accretion of mass in an astrophysical model

Authors 1

Affiliations

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

Abstract

We study asymptotic behavior of radial solutions of a nonlocal Fokker-Planck equation describing the evolution of self-attracting particles. In particular, we consider stationary solutions in balls and in the whole space, self-similar solutions defined globally in time, blowing up self-similar solutions, and singularities of solutions that blow up in a finite time.

Keywords

ENG
asymptotic behavior, radial solutions, nonlinear parabolic equation

Bibliography

  1. P. Biler, The Cauchy problem and self-similar solutions for a nonlinear parabolic equation, Studia Math. 114 (1995), 181-205.
  2. P. Biler, Existence and nonexistence of solutions for a model of gravitational interaction of particles, III, Colloq. Math. 68 (1995), 229-239.
  3. P. Biler, W. Hebisch and T. Nadzieja, The Debye system: existence and large time behavior of solutions, Nonlinear Anal. 23 (1994), 1189-1209.
  4. P. Biler, D. Hilhorst and T. Nadzieja, Existence and nonexistence of solutions for a model of gravitational interaction of particles, II, Colloq. Math. 67 (1994), 297-308.
  5. P. Biler and T. Nadzieja, A class of nonlocal parabolic problems occurring in statistical mechanics, ibid. 66 (1993), 131-145.
  6. P. Biler and T. Nadzieja, Existence and nonexistence of solutions for a model of gravitational interaction of particles, I, ibid. 66 (1994), 319-334.
  7. A. Krzywicki and T. Nadzieja, Some results concerning the Poisson-Boltzmann equation, Zastos. Mat. 21 (1991), 265-272.
  8. A. Krzywicki and T. Nadzieja, A note on the Poisson-Boltzmann equation, ibid. 21 (1993), 591-595.
  9. T. Nadzieja, A model of a radially symmetric cloud of self-attracting particles, Appl. Math. (Warsaw) 23 (1995), 169-178.
  10. G. Wolansky, On steady distributions of self-attracting clusters under friction and fluctuations, Arch. Rational Mech. Anal. 119 (1992), 355-391.
  11. G. Wolansky, On the evolution of self-interacting clusters and applications to semilinear equations with exponential nonlinearity, J. Analyse Math. 59 (1992), 251-272.
Applicationes Mathematicae
1995-1996/23/2
Export to PBN, Opens in new tab
Pages:
179-189
Main language of publication
English
Received
1994-09-13
Published
1995
Exact and natural sciences