Abstract
A large number of identical particles in self-interaction in the torus may be described by the Vlasov-Poisson system of equations. Assuming the initial velocities to be bounded, one considers the asymptotic behaviour of the maximum velocity in the cloud and shows it grows at most like a power one third of the time variable.
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References
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Pallard, C. About the Velocities of Self-interacting Particles in the 1-D Torus. J Stat Phys 144, 826–830 (2011). https://doi.org/10.1007/s10955-011-0295-7
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DOI: https://doi.org/10.1007/s10955-011-0295-7