Archive for Rational Mechanics and Analysis

, Volume 119, Issue 4, pp 355–391 | Cite as

On steady distributions of self-attracting clusters under friction and fluctuations

  • G. Wolansky
Article

Abstract

We consider the Vlasov-Fokker-Planek equation with a Newtonian, attracting potential and study its stationary solutions, given by the generalized Lane-Emden equation. In a two-dimensional domain we obtain the existence of a critical mass beyond which the system may admit a gravitational collapse. For a one-dimensional model we prove some results on existence, uniqueness, stability and symmetry-breaking of stationary solutions.

Keywords

Neural Network Complex System Nonlinear Dynamics Stationary Solution Electromagnetism 

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Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • G. Wolansky
    • 1
  1. 1.Department of Mathematics TechnionIsrael Institute of TechnologyHaifaIsrael

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