In this paper, we consider the stochastic dynamics of a finite system of particles in a finite volume (Kac-like particle system) which annihilate with probability α∈ (0,1) or collide elastically with probability 1 - α. We first establish the well-posedness of the particle system which exhibits no conserved quantities. We rigorously prove that, in some mean-field limit, a suitable hierarchy of kinetic equations is recovered for which tensorized solution to the homogenous Boltzmann with annihilation is a solution. For bounded collision kernels, this shows in particular that propagation of chaos holds true. Furthermore, we make conjectures about the limit behaviour of the particle system when hard-sphere interactions are taken into account.

A Kac Model for Kinetic Annihilation

Nota A.;Pezzotti F.
2020

Abstract

In this paper, we consider the stochastic dynamics of a finite system of particles in a finite volume (Kac-like particle system) which annihilate with probability α∈ (0,1) or collide elastically with probability 1 - α. We first establish the well-posedness of the particle system which exhibits no conserved quantities. We rigorously prove that, in some mean-field limit, a suitable hierarchy of kinetic equations is recovered for which tensorized solution to the homogenous Boltzmann with annihilation is a solution. For bounded collision kernels, this shows in particular that propagation of chaos holds true. Furthermore, we make conjectures about the limit behaviour of the particle system when hard-sphere interactions are taken into account.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11697/151265
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 0
social impact