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## Colloquium Mathematicum

1994 | 67 | 2 | 297-308
Tytuł artykułu

### Existence and nonexistence of solutions for a model of gravitational interaction of particles, II

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We study the existence and nonexistence in the large of radial solutions to a parabolic-elliptic system with natural (no-flux) boundary conditions describing the gravitational interaction of particles. The blow-up of solutions defined in the n-dimensional ball with large initial data is connected with the nonexistence of radial stationary solutions with a large mass.
Słowa kluczowe
EN
Czasopismo
Rocznik
Tom
Numer
Strony
297-308
Opis fizyczny
Daty
wydano
1994
otrzymano
1994-01-31
Twórcy
autor
• Mathematical Institute, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
autor
• Laboratoire d'Analyse Numérique d'Orsay, Université de Paris-Sud, bât. 425, 91405 Orsay, France
autor
• Mathematical Institute, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
Bibliografia
• [1] M.-F. Bidaut-Véron and L. Véron, Nonlinear elliptic equations on compact Riemannian manifolds and asymptotics of Emden equations, Invent. Math. 106 (1991), 489-539.
• [2] P. Biler, Blowup in nonlinear parabolic equations, Colloq. Math. 58 (1989), 85-110.
• [3] P. Biler, Blow-up in the porous medium equation, in: Recent Advances in Nonlinear Elliptic and Parabolic Problems, Proc. Internat. Conf. Nancy, 1988, P. Bénilan, M. Chipot, L. C. Evans and M. Pierre (eds.), Pitman Res. Notes in Math. 208, Longman, Harlow, 1989, 28-38.
• [4] P. Biler, Existence and asymptotics of solutions for a parabolic-elliptic system with nonlinear no-flux boundary conditions, Nonlinear Anal. 19 (1992), 1121-1136.
• [5] P. Biler and T. Nadzieja, Existence and nonexistence of solutions for a model of gravitational interaction of particles, I, Colloq. Math. 66 (1994), 319-334.
• [6] E. Caglioti, P.-L. Lions, C. Marchioro and M. Pulvirenti, A special class of stationary flows for two-dimensional Euler equations: a statistical mechanics description, Comm. Math. Phys. 143 (1992), 501-525.
• [7] A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, N.J., 1964.
• [8] Y. Giga and R. V. Kohn, Asymptotically self-similar blow-up of semilinear heat equations, Comm. Pure Appl. Math. 38 (1985), 297-319.
• [9] D. Hilhorst, A nonlinear evolution problem arising in the physics of ionized gases, SIAM J. Math. Anal. 13 (1982), 16-39.
• [10] D. D. Joseph and T. S. Lundgren, Quasilinear Dirichlet problems driven by positive sources, Arch. Rational Mech. Anal. 49 (1973), 241-269.
• [11] A. Krzywicki and T. Nadzieja, Some results concerning the Poisson-Boltzmann equation, Zastos. Mat. 21 (1991), 265-272.
• [12] A. Krzywicki and T. Nadzieja, A nonstationary problem in the theory of electrolytes, Quart. Appl. Math. 50 (1992), 105-107.
• [13] A. Krzywicki and T. Nadzieja, A note on the Poisson-Boltzmann equation, Zastos. Mat. 21 (1993), 591-595.
• [14] O. A. Ladyženskaja, V. A. Solonnikov and N. N. Ural'ceva, Linear and Quasilinear Equations of Parabolic Type, Amer. Math. Soc., Providence, R.I., 1988.
• [15] K. Nagasaki and T. Suzuki, Radial and nonradial solutions for the nonlinear eigenvalue problem $Δu + λe^u=0$ on annuli in $ℝ^2$, J. Differential Equations 87 (1990), 144-168.
• [16] K. Nagasaki and T. Suzuki, Radial solutions for $Δu + λe^u = 0$ on annuli in higher dimensions, ibid. 100 (1992), 137-161.
• [17] F. Pacard, Radial and nonradial solutions of -Δu=λf(u) on an annulus of $ℝ^n$, n ≥ 3, ibid. 101 (1993), 103-138.
• [18] T. Suzuki, Global analysis for a two-dimensional elliptic eigenvalue problem with the exponential nonlinearity, Ann. Inst. Henri Poincaré Anal. Non Linéaire 9 (1992), 367-398.
• [19] G. Wolansky, On steady distributions of self-attracting clusters under friction and fluctuations, Arch. Rational Mech. Anal. 119 (1992), 355-391.
• [20] G. Wolansky, On the evolution of self-interacting clusters and applications to semilinear equations with exponential nonlinearity, J. Analyse Math. 59 (1992), 251-272.
Typ dokumentu
Bibliografia
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