### Abstract

Lingua originale | English |
---|---|

pagine (da-a) | 633-668 |

Numero di pagine | 36 |

Rivista | Kinetic and Related Models |

Volume | 4 |

Stato di pubblicazione | Published - 2011 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Numerical Analysis
- Modelling and Simulation

### Cita questo

*Kinetic and Related Models*,

*4*, 633-668.

**A simple particle model for a system of coupled equations with absorbing
collision term.** / Ricci, Valeria; Bernardin, Cédric.

Risultato della ricerca: Article

*Kinetic and Related Models*, vol. 4, pagg. 633-668.

}

TY - JOUR

T1 - A simple particle model for a system of coupled equations with absorbing collision term

AU - Ricci, Valeria

AU - Bernardin, Cédric

PY - 2011

Y1 - 2011

N2 - We study a particle model for a simple system of partial differential equations describing, 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 system where 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. We prove 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 11 and ad εζ → 0, for κ ∈ (0, 1/2) and ζ ∈ (0, 2 − 2d ), where a^d_n is the effective range of the obstacles and n is the total number of light particles.

AB - We study a particle model for a simple system of partial differential equations describing, 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 system where 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. We prove 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 11 and ad εζ → 0, for κ ∈ (0, 1/2) and ζ ∈ (0, 2 − 2d ), where a^d_n is the effective range of the obstacles and n is the total number of light particles.

KW - Interacting particle systems, large numbers limit, absorption

UR - http://hdl.handle.net/10447/68287

M3 - Article

VL - 4

SP - 633

EP - 668

JO - Kinetic and Related Models

JF - Kinetic and Related Models

SN - 1937-5093

ER -