A model of a radially symmetric cloud of self-attracting particles

Tadeusz Nadzieja

Applicationes Mathematicae (1995)

  • Volume: 23, Issue: 2, page 169-178
  • ISSN: 1233-7234

Abstract

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We consider a parabolic equation which describes the gravitational interaction of particles. Existence of solutions and their convergence to stationary states are studied.

How to cite

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Nadzieja, Tadeusz. "A model of a radially symmetric cloud of self-attracting particles." Applicationes Mathematicae 23.2 (1995): 169-178. <http://eudml.org/doc/219123>.

@article{Nadzieja1995,
abstract = {We consider a parabolic equation which describes the gravitational interaction of particles. Existence of solutions and their convergence to stationary states are studied.},
author = {Nadzieja, Tadeusz},
journal = {Applicationes Mathematicae},
keywords = {asymptotic behavior; cloud of particles; nonlinear parabolic equation; radially symmetric solutions; existence; gravitational interaction of particles; stationary states},
language = {eng},
number = {2},
pages = {169-178},
title = {A model of a radially symmetric cloud of self-attracting particles},
url = {http://eudml.org/doc/219123},
volume = {23},
year = {1995},
}

TY - JOUR
AU - Nadzieja, Tadeusz
TI - A model of a radially symmetric cloud of self-attracting particles
JO - Applicationes Mathematicae
PY - 1995
VL - 23
IS - 2
SP - 169
EP - 178
AB - We consider a parabolic equation which describes the gravitational interaction of particles. Existence of solutions and their convergence to stationary states are studied.
LA - eng
KW - asymptotic behavior; cloud of particles; nonlinear parabolic equation; radially symmetric solutions; existence; gravitational interaction of particles; stationary states
UR - http://eudml.org/doc/219123
ER -

References

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  1. [1] P. Biler, The Cauchy problem and self-similar solutions for a nonlinear parabolic equation, preprint 1994. Zbl0829.35044
  2. [2] 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
  3. [3] P. Biler and T. Nadzieja, A class of nonlocal parabolic problems occurring in statistical mechanics, ibid. 66 (1993), 131-145. Zbl0818.35046
  4. [4] 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
  5. [5] W. Chen and C. Li, Classification of solutions of some nonlinear elliptic equations, Duke Math. J. 63 (1991), 615-622. Zbl0768.35025
  6. [6] A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, N.J., 1964. Zbl0144.34903
  7. [7] E. Hopf, The partial differential equation u_t + uu_x=u_xx, Comm. Pure Appl. Math. 3 (1950), 201-230. Zbl0039.10403
  8. [8] A. Krzywicki and T. Nadzieja, Some results concerning the Poisson-Boltzmann equation, Zastos. Mat. 21 (1991), 265-272. Zbl0756.35029
  9. [9] A. Krzywicki and T. Nadzieja, A note on the Poisson-Boltzmann equation, ibid. 21 (1993), 591-595. Zbl0780.35033
  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

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