On steady distributions of self-attracting clusters under friction and fluctuations |
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Authors: | G. Wolansky |
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Affiliation: | (1) Department of Mathematics Technion, Israel Institute of Technology, 32000 Haifa, Israel |
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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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