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A Model of Heat Conduction

Collet, P. ; Eckmann, J.

In: Communications in Mathematical Physics, 2009, vol. 287, no. 3, p. 1015-1038

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    Titre
    • A Model of Heat Conduction
    Auteur
    • Collet, P.. Centre de Physique Théorique, CNRS UMR 7644, Ecole Polytechnique, F-91128, Palaiseau Cedex, France
    • Eckmann, J.. Département de Physique Théorique et Section de Mathématiques, Université de Genève, CH-1211, Genève 4, Switzerland
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • Communications in Mathematical Physics, 2009, vol. 287, no. 3, p. 1015-1038. Springer-Verlag
    Autre version électronique
    Classification
    • Mathématiques
    Identifiant OAI-PMH
    • oai:doc.rero.ch:322052
    Summary
    In this paper, we first define a deterministic particle model for heat conduction. It consists of a chain of N identical subsystems, each of which contains a scatterer and with particles moving among these scatterers. Based on this model, we then derive heuristically, in the limit of N → ∞ and decreasing scattering cross-section, a Boltzmann equation for this limiting system. This derivation is obtained by a closure argument based on memory loss between collisions. We then prove that the Boltzmann equation has, for stochastic driving forces at the boundary, close to Maxwellians, a unique non-equilibrium steady state