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.
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Communicated by K.Kirchgässner
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Wolansky, G. On steady distributions of self-attracting clusters under friction and fluctuations. Arch. Rational Mech. Anal. 119, 355–391 (1992). https://doi.org/10.1007/BF01837114
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DOI: https://doi.org/10.1007/BF01837114