Kinetic and hydrodynamic equations for granular media
In this lecture i present some open mathematical problems concerning some PDE arising in the study of one-dimensional models for granular media.
Il sesto problema di Hilbert e le moderne teorie cinetiche.
In questo contributo si discute qualche problema connesso alla derivazione delle equazioni cinetiche a partire dalla meccanica dei sistemi di particelle.
On the Plasma-Charge problem
This short report is a review on recent results of S. Caprino, C. Marchioro, E. Miot and the author on the initial value problem associated to the evolution of a continuous distribution of charges (plasma) in presence of a finite number of point charges.
On the one-dimensional Boltzmann equation for granular flows
We consider a Boltzmann equation for inelastic particles on the line and prove existence and uniqueness for the solutions.
On the Singularities of the Newtonian two dimensional N-body Problem
Si considera un sistema bidimensionale di particelle interagenti tramite un potenziale di Newton o di Coulomb e si mostra che l’insieme delle condizioni iniziali che in un tempo finito possono condurre a delle singolarità possiede misura di Lebesgue nulla.
On the Singularities of the Newtonian two dimensional N-body Problem
Si considera un sistema bidimensionale di particelle interagenti tramite un potenziale di Newton o di Coulomb e si mostra che l’insieme delle condizioni iniziali che in un tempo finito possono condurre a delle singolarità possiede misura di Lebesgue nulla.
On the one-dimensional Boltzmann equation for granular flows
We consider a Boltzmann equation for inelastic particles on the line and prove existence and uniqueness for the solutions.
A Kinetic equation for granular media
Superstable interactions in quantum statistical mechanics : Maxwell-Boltzmann statistics
A kinetic equation for granular media
In this short note we correct a conceptual error in the heuristic derivation of a kinetic equation used for the description of a one-dimensional granular medium in the so called quasi-elastic limit, presented by the same authors in reference[1]. The equation we derived is however correct so that, the rigorous analysis on this equation, which constituted the main purpose of that paper, remains unchanged.
On the motion of a body in thermal equilibrium immersed in a perfect gas
We consider a body immersed in a perfect gas and moving under the action of a constant force. Body and gas are in thermal equilibrium. We assume a stochastic interaction body/medium: when a particle of the medium hits the body, it is absorbed and immediately re-emitted with a Maxwellian distribution. This system gives rise to a microscopic model of friction. We study the approach of the body velocity to the limiting velocity and prove that, under suitable smallness assumptions, the approach...
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