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

• Autorzy: Tadeusz Nadzieja
• Języki publikacji: EN

Abstrakty

EN

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

Słowa kluczowe

EN

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

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 1995-1996
• Tom: 23
• Numer: 2
• Strony: 169-178

Daty

wydano

1995

otrzymano

1994-07-25

Twórcy

autor

Tadeusz Nadzieja

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

Bibliografia

• [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.