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

Colloquium Mathematicae (1993)

- Volume: 66, Issue: 2, page 319-334
- ISSN: 0010-1354

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topBiler, Piotr, and Nadzieja, Tadeusz. "Existence and nonexistence of solutions for a model of gravitational interaction of particles, I." Colloquium Mathematicae 66.2 (1993): 319-334. <http://eudml.org/doc/210252>.

@article{Biler1993,

abstract = {We study the existence of stationary and evolution solutions to a parabolic-elliptic system with natural (no-flux) boundary conditions describing the gravitational interaction of particles.},

author = {Biler, Piotr, Nadzieja, Tadeusz},

journal = {Colloquium Mathematicae},

keywords = {nonlinear boundary conditions; stationary solutions; global existence of solutions; parabolic-elliptic system; nonlinear no-flux condition; blow-up; Chandrasekhar equation},

language = {eng},

number = {2},

pages = {319-334},

title = {Existence and nonexistence of solutions for a model of gravitational interaction of particles, I},

url = {http://eudml.org/doc/210252},

volume = {66},

year = {1993},

}

TY - JOUR

AU - Biler, Piotr

AU - Nadzieja, Tadeusz

TI - Existence and nonexistence of solutions for a model of gravitational interaction of particles, I

JO - Colloquium Mathematicae

PY - 1993

VL - 66

IS - 2

SP - 319

EP - 334

AB - We study the existence of stationary and evolution solutions to a parabolic-elliptic system with natural (no-flux) boundary conditions describing the gravitational interaction of particles.

LA - eng

KW - nonlinear boundary conditions; stationary solutions; global existence of solutions; parabolic-elliptic system; nonlinear no-flux condition; blow-up; Chandrasekhar equation

UR - http://eudml.org/doc/210252

ER -

## References

top- [1] R. A. Adams, Sobolev Spaces, Academic Press, New York, 1975.
- [2] F. Bavaud, Equilibrium properties of the Vlasov functional: the generalized Poisson-Boltzmann-Emden equation, Rev. Modern Phys. 63 (1991), 129-149.
- [3] 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.
- [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. Zbl0781.35025
- [5] P. Biler, W. Hebisch and T. Nadzieja, The Debye system: existence and large time behavior of solutions, Mathematical Institute, University of Wrocław, Report no. 23 (1992), 1-24 . Zbl0814.35054
- [6] P. Biler, D. Hilhorst and T. Nadzieja, Existence and nonexistence of solutions for a model of gravitational interaction of particles, II, preprint, 1993. Zbl0832.35015
- [7] P. Biler and T. Nadzieja, A class of nonlocal parabolic problems occurring in statistical mechanics, Colloq. Math. 66 (1993), 131-145. Zbl0818.35046
- [8] 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. Zbl0745.76001
- [9] P. Cherrier, Meilleures constantes dans des inégalités relatives aux espaces de Sobolev, Bull. Sci. Math. 108 (1984), 225-262. Zbl0547.58017
- [10] R. Dautray and J.-L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, Vol. 1, Springer, Berlin, 1990. Zbl0683.35001
- [11] D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd ed., Springer, Berlin, 1983. Zbl0562.35001
- [12] A. Krzywicki and T. Nadzieja, Some results concerning the Poisson-Boltzmann equation, Zastos. Mat. 21 (1991), 265-272. Zbl0756.35029
- [13] A. Krzywicki and T. Nadzieja, A nonstationary problem in the theory of electrolytes, Quart. Appl. Math. 50 (1992), 105-107. Zbl0754.35142
- [14] A. Krzywicki and T. Nadzieja, A note on the Poisson-Boltzmann equation, Zastos. Mat. 21 (1993), 591-595. Zbl0780.35033
- [15] 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.
- [16] T. Suzuki, Global analysis for a two-dimensional elliptic eigenvalue problem with the exponential nonlinearity, Ann. Inst. H. Poincaré Anal. Non Linéaire 9 (1992), 367-398. Zbl0785.35045
- [17] S. Wang, Some nonlinear elliptic equations with subcritical growth and critical behavior, Houston J. Math. 16 (1990), 559-572. Zbl0741.35016
- [18] G. Wolansky, On steady distributions of self-attracting clusters under friction and fluctuations, Arch. Rational Mech. Anal. 119 (1992), 355-391. Zbl0774.76069
- [19] G. Wolansky, On the evolution of self-interacting clusters and applications to semilinear equations with exponential nonlinearity, J. Analyse Math. 59 (1992), 251-272. Zbl0806.35134

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