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On the asymptotic growth of the solutions of the Vlasov–Poisson system. (English) Zbl 0782.35079
The Vlasov-Poisson equation is the well known integro-differential equation which describes the dynamics of a galaxy or a plasma. Its difficulty is due to the presence of a singular kernel in the integral which defines the Newtonian or Coulomb force, depending upon the case.
In order to study this equation, the author regularizes this kernel by using a perturbation scheme. He proves a global theorem for this modified equation, and then he makes the perturbation parameter tend to zero. Moreover he shows that the velocities of the particles (stars or ions) grow like $$O(t\log^{11/14} t)$$ in time.

MSC:
 35Q72 Other PDE from mechanics (MSC2000) 85A05 Galactic and stellar dynamics 82D10 Statistical mechanical studies of plasmas
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References:
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