139 citations · 453 across the 6 of their papers we have counts for
6 papers
A new interaction potential for swarming models
J. A. Carrillo, S. Martin, V. Panferov
We consider a self-propelled particle system which has been used to describe certain types of collective motion of animals, such as fish schools and bird flocks. Interactions betwe…
Hydrodynamic models of self-organized dynamics: derivation and existence theory
Pierre Degond, Jian-Guo Liu, Sébastien Motsch +1
This paper is concerned with the derivation and analysis of hydrodynamic models for systems of self-propelled particles subject to alignment interaction and attraction-repulsion. T…
The McKean-Vlasov Equation in Finite Volume
Lincoln Chayes, Vladislav Panferov
We study the McKean--Vlasov equation on the finite tori of length scale in --dimensions. We derive the necessary and sufficient conditions for the existence of a phase trans…
Upper Maxwellian bounds for the spatially homogeneous Boltzmann equation
I. M. Gamba, V. Panferov, C. Villani
For the spatially homogeneous Boltzmann equation with cutoff hard potentials it is shown that solutions remain bounded from above, uniformly in time, by a Maxwellian distribution,…
Moment inequalities and high-energy tails for the Boltzmann equations with inelastic interactions
Alexander V. Bobylev, Irene M. Gamba, Vladislav A. Panferov
We study the high-energy asymptotics of the steady velocity distributions for model systems of granular media in various regimes. The main results obtained are integral estimates o…
On the Boltzmann equation for diffusively excited granular media
Irene M. Gamba, Vladislav Panferov, Cedric Villani
We study the Boltzmann equation for a space-homogeneous gas of inelastic hard spheres, with a diffusive term representing a random background forcing. Under the assumption that the…