# 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

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- [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
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- [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
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- [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

## Citations in EuDML Documents

top- Ryo Kobayashi, Masakazu Yamamoto, Shuichi Kawashima, Asymptotic stability of stationary solutions to the drift-diffusion model in the whole space
- Piotr Biler, Danielle Hilhorst, Tadeusz Nadzieja, Existence and nonexistence of solutions for a model of gravitational interaction of particles, II
- Piotr Biler, Existence and nonexistence of solutions for a model of gravitational interaction of particles, III
- Piotr Biler, Tadeusz Nadzieja, Existence and nonexistence of solutions for a model of gravitational interaction of particles, I
- Tadeusz Nadzieja, A model of a radially symmetric cloud of self-attracting particles
- Piotr Biler, Tadeusz Nadzieja, Growth and accretion of mass in an astrophysical model, II
- Piotr Biler, The Cauchy problem and self-similar solutions for a nonlinear parabolic equation
- Andrzej Krzywicki, Tadeusz Nadzieja, Nonlocal elliptic problems
- Andrzej Raczyński, On a nonlocal elliptic problem
- Piotr Biler, Growth and accretion of mass in an astrophysical model

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