Growth and accretion of mass in an astrophysical model

Piotr Biler

Applicationes Mathematicae (1995)

  • Volume: 23, Issue: 2, page 179-189
  • ISSN: 1233-7234

Abstract

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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.

How to cite

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Biler, Piotr. "Growth and accretion of mass in an astrophysical model." Applicationes Mathematicae 23.2 (1995): 179-189. <http://eudml.org/doc/219124>.

@article{Biler1995,
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.},
author = {Biler, Piotr},
journal = {Applicationes Mathematicae},
keywords = {asymptotic behavior; radial solutions; nonlinear parabolic equation; Fokker-Planck equation; evolution of self-attracting particles; stationary solutions; self-similar solutions; singularities},
language = {eng},
number = {2},
pages = {179-189},
title = {Growth and accretion of mass in an astrophysical model},
url = {http://eudml.org/doc/219124},
volume = {23},
year = {1995},
}

TY - JOUR
AU - Biler, Piotr
TI - Growth and accretion of mass in an astrophysical model
JO - Applicationes Mathematicae
PY - 1995
VL - 23
IS - 2
SP - 179
EP - 189
AB - 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.
LA - eng
KW - asymptotic behavior; radial solutions; nonlinear parabolic equation; Fokker-Planck equation; evolution of self-attracting particles; stationary solutions; self-similar solutions; singularities
UR - http://eudml.org/doc/219124
ER -

References

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  1. [1] P. Biler, The Cauchy problem and self-similar solutions for a nonlinear parabolic equation, Studia Math. 114 (1995), 181-205. Zbl0829.35044
  2. [2] P. Biler, Existence and nonexistence of solutions for a model of gravitational interaction of particles, III, Colloq. Math. 68 (1995), 229-239. Zbl0836.35076
  3. [3] P. Biler, W. Hebisch and T. Nadzieja, The Debye system: existence and large time behavior of solutions, Nonlinear Anal. 23 (1994), 1189-1209. Zbl0814.35054
  4. [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. Zbl0832.35015
  5. [5] P. Biler and T. Nadzieja, A class of nonlocal parabolic problems occurring in statistical mechanics, ibid. 66 (1993), 131-145. Zbl0818.35046
  6. [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. Zbl0817.35041
  7. [7] A. Krzywicki and T. Nadzieja, Some results concerning the Poisson-Boltzmann equation, Zastos. Mat. 21 (1991), 265-272. Zbl0756.35029
  8. [8] A. Krzywicki and T. Nadzieja, A note on the Poisson-Boltzmann equation, ibid. 21 (1993), 591-595. Zbl0780.35033
  9. [9] T. Nadzieja, A model of a radially symmetric cloud of self-attracting particles, Appl. Math. (Warsaw) 23 (1995), 169-178. Zbl0839.35110
  10. [10] G. Wolansky, On steady distributions of self-attracting clusters under friction and fluctuations, Arch. Rational Mech. Anal. 119 (1992), 355-391. Zbl0774.76069
  11. [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. Zbl0806.35134

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