| Abstract: |
| We study the limit as the number of particles goes to infinity
of the dynamics of a system of $N$ particles moving through velocity fields of convolution type
and subject to an additional separation constraint (hard-spheres model).
This can be formalised by introducing a suitable control problem and assuming that the velocity fields are
Lipschitz regular. The limiting dynamics is then described by a particle density $\rho(t,x)$ satisfying a
suitable continuity equation of Vlasov type an uniform upper bound. |
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