A simple particle model for a system of coupled equations with absorbingcollision term

Valeria Ricci, Cédric Bernardin

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1 Citation (Scopus)

Abstract

We study a particle model for a simple system of partial differential equationsdescribing, in dimension d ≥ 2, a two component mixture where light particles move in a medium of absorbing, fixed obstacles; the system consists in a transport and a reaction equation coupled through pure absorption collision terms. We consider a particle systemwhere the obstacles, of radius ε, become inactive at a rate related to the number of light particles travelling in their range of influence at a given time and the light particles are instantaneously absorbed at the first time they meet the physical boundary of an obstacle; elements belonging to the same species do not interact among themselves. Weprove the convergence (a.s. w.r.t. the product measure associated to the initial datum for the light particle component) of the densities describing the particle system to the solution of the system of partial differential equations in the asymptotics a^d_n−κ → 0 n 11and ad εζ → 0, for κ ∈ (0, 1/2) and ζ ∈ (0, 2 − 2d ), where a^d_n is the effective range of theobstacles and n is the total number of light particles.
Original languageEnglish
Pages (from-to)633-668
Number of pages36
JournalKinetic and Related Models
Volume4
Publication statusPublished - 2011

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modelling and Simulation

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