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English

A model of heat conduction

Published inCommunications in Mathematical Physics, vol. 287, no. 3, p. 1015-1038
Publication date2009
Abstract

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.

Citation (ISO format)
COLLET, P., ECKMANN, Jean-Pierre. A model of heat conduction. In: Communications in Mathematical Physics, 2009, vol. 287, n° 3, p. 1015–1038. doi: 10.1007/s00220-008-0691-2
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ISSN of the journal1432-0916
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