ArticleOriginal scientific text

Title

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

Authors 1

Affiliations

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

Abstract

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

Keywords

asymptotic behavior, cloud of particles, nonlinear parabolic equation, radially symmetric solutions

Bibliography

  1. P. Biler, The Cauchy problem and self-similar solutions for a nonlinear parabolic equation, preprint 1994.
  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.
  3. P. Biler and T. Nadzieja, A class of nonlocal parabolic problems occurring in statistical mechanics, ibid. 66 (1993), 131-145.
  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.
  5. W. Chen and C. Li, Classification of solutions of some nonlinear elliptic equations, Duke Math. J. 63 (1991), 615-622.
  6. A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, N.J., 1964.
  7. E. Hopf, The partial differential equation u_t + uu_x=u_xx, Comm. Pure Appl. Math. 3 (1950), 201-230.
  8. A. Krzywicki and T. Nadzieja, Some results concerning the Poisson-Boltzmann equation, Zastos. Mat. 21 (1991), 265-272.
  9. A. Krzywicki and T. Nadzieja, A note on the Poisson-Boltzmann equation, ibid. 21 (1993), 591-595.
  10. G. Wolansky, On steady distributions of self-attracting clusters under friction and fluctuations, Arch. Rational Mech. Anal. 119 (1992), 355-391.
Pages:
169-178
Main language of publication
English
Received
1994-07-25
Published
1995
Exact and natural sciences