Growth and accretion of mass in an astrophysical model, II

• Autorzy: Piotr Biler , Tadeusz Nadzieja
• Języki publikacji: EN

Abstrakty

EN

Radially symmetric solutions of a nonlocal Fokker-Planck equation describing the evolution of self-attracting particles in a bounded container are studied. Conditions ensuring either global-in-time existence of solutions or their finite time blow up are given.

Słowa kluczowe

EN

radial solutions; global and blowing up solutions; nonlinear parabolic equation

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 1995-1996
• Tom: 23
• Numer: 3
• Strony: 351-361

Daty

wydano

1995

otrzymano

1995-01-24

Twórcy

autor

Piotr Biler

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

autor

Tadeusz Nadzieja

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

Bibliografia

• [1] P. Biler, Growth and accretion of mass in an astrophysical model, Appl. Math. (Warsaw) 23 (1995), 179-189.
• [2] P. Biler, Local and global solutions of a nonlinear nonlocal parabolic problem, in: Proc. of the Banach Center minisemester 'Nonlinear Analysis and Applications', to appear.
• [3] P. Biler, Existence and nonexistence of solutions for a model of gravitational interaction of particles, III, Colloq. Math. 68 (1995), 229-339.
• [4] P. Biler, D. Hilhorst and T. Nadzieja, Existence and nonexistence of solutions for a model of gravitational interaction of particles, II, ibid. 67 (1994), 297-308.
• [5] P. Biler and T. Nadzieja, Existence and nonexistence of solutions for a model of gravitational interaction of particles, I, ibid. 66 (1994), 319-334.
• [6] A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, N.J., 1964.
• [7] W. Jäger and S. Luckhaus, On explosions of solutions to a system of partial differential equations modelling chemotaxis, Trans. Amer. Math. Soc. 329 (1992), 819-824.
• [8] S. Karlin and H. M. Taylor, A Second Course in Stochastic Processes, Academic Press, New York, 1981.
• [9] O. A. Ladyženskaja [O. A. Ladyzhenskaya], V. A. Solonnikov and N. N. Ural'ceva [N. N. Ural'tseva], Linear and Quasilinear Equations of Parabolic Type, Amer. Math. Soc., Providence, R.I., 1988.
• [10] T. Nadzieja, A model of a radially symmetric cloud of self-attracting particles, Appl. Math. (Warsaw) 23 (1995), 169-178.
• [11] G. Wolansky, On steady distributions of self-attracting clusters under friction and fluctuations, Arch. Rational Mech. Anal. 119 (1992), 355-391.
• [12] G. Wolansky, On the evolution of self-interacting clusters and applications to semilinear equations with exponential nonlinearity, J. Anal. Math. 59 (1992), 251-272.