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arXiv · 1904.03447

A Kac model for kinetic annihilation

Bertrand Lods·Alessia Nota·Federica Pezzotti
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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 $α\in (0,1)$ 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 thermodynamic 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.

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Bertrand Lods, Alessia Nota, Federica Pezzotti. 2019-04-06. A Kac model for kinetic annihilation. https://doi.org/10.1007/s00332-020-09614-z

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