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

Piotr Biler; Tadeusz Nadzieja

Colloquium Mathematicae (1993)

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

Abstract

top
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.

How to cite

top

Biler, 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. [1] R. A. Adams, Sobolev Spaces, Academic Press, New York, 1975. 
  2. [2] F. Bavaud, Equilibrium properties of the Vlasov functional: the generalized Poisson-Boltzmann-Emden equation, Rev. Modern Phys. 63 (1991), 129-149. 
  3. [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. [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. [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. [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. [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. [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. [9] P. Cherrier, Meilleures constantes dans des inégalités relatives aux espaces de Sobolev, Bull. Sci. Math. 108 (1984), 225-262. Zbl0547.58017
  10. [10] R. Dautray and J.-L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, Vol. 1, Springer, Berlin, 1990. Zbl0683.35001
  11. [11] D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd ed., Springer, Berlin, 1983. Zbl0562.35001
  12. [12] A. Krzywicki and T. Nadzieja, Some results concerning the Poisson-Boltzmann equation, Zastos. Mat. 21 (1991), 265-272. Zbl0756.35029
  13. [13] A. Krzywicki and T. Nadzieja, A nonstationary problem in the theory of electrolytes, Quart. Appl. Math. 50 (1992), 105-107. Zbl0754.35142
  14. [14] A. Krzywicki and T. Nadzieja, A note on the Poisson-Boltzmann equation, Zastos. Mat. 21 (1993), 591-595. Zbl0780.35033
  15. [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. [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. [17] S. Wang, Some nonlinear elliptic equations with subcritical growth and critical behavior, Houston J. Math. 16 (1990), 559-572. Zbl0741.35016
  18. [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. [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
  1. Ryo Kobayashi, Masakazu Yamamoto, Shuichi Kawashima, Asymptotic stability of stationary solutions to the drift-diffusion model in the whole space
  2. Piotr Biler, Danielle Hilhorst, Tadeusz Nadzieja, Existence and nonexistence of solutions for a model of gravitational interaction of particles, II
  3. Piotr Biler, Existence and nonexistence of solutions for a model of gravitational interaction of particles, III
  4. Piotr Biler, Tadeusz Nadzieja, Existence and nonexistence of solutions for a model of gravitational interaction of particles, I
  5. Tadeusz Nadzieja, A model of a radially symmetric cloud of self-attracting particles
  6. Piotr Biler, Tadeusz Nadzieja, Growth and accretion of mass in an astrophysical model, II
  7. Piotr Biler, The Cauchy problem and self-similar solutions for a nonlinear parabolic equation
  8. Andrzej Krzywicki, Tadeusz Nadzieja, Nonlocal elliptic problems
  9. Andrzej Raczyński, On a nonlocal elliptic problem
  10. Piotr Biler, Growth and accretion of mass in an astrophysical model

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.