Some remarks about the scaling of systems of reactive Boltzmann equations

Marzia Bisi; Laurent Desvillettes

doi:10.3934/krm.2008.1.515

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2008, Volume 1, Issue 4: 515-520. Doi: 10.3934/krm.2008.1.515

This issue Previous Article Integral estimates for a linear singular operator linked with Boltzmann operators part II: High singularities $1\le\nu<2$ Next Article On some properties of linear and linearized Boltzmann collision operators for hard spheres

Some remarks about the scaling of systems of reactive Boltzmann equations

Marzia Bisi^1, and
Laurent Desvillettes^2,

1.
Dipartimento di Matematica, Università di Parma, Viale G.P. Usberti 53/A, I-43100 Parma
2.
ENS Cachan, CMLA, IUF & CNRS, PRES UniverSud, 61, Av. du Pdt Wilson, 94235 Cachan Cedex

Received: July 31, 2008

Revised: August 31, 2008

Published: October 2008

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Abstract

An asymptotics leading from the reactive Boltzmann equation towards reaction--diffusion equations has been introduced in [1] (cf. also [10], for an analogous scaling starting from reactive BGK equations). We propose here a justification of this asymptotics, at the formal level, based on a non--dimensional form of the original equations.

Keywords:

Reactive Boltzmann equations; Reaction--diffusion systems.

Mathematics Subject Classification: 82C40, 76P05, 35K57.

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