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Article Dans Une Revue Nonlinearity Année : 2014

Kinetic models coupled with Gaussian thermostats: macroscopic frameworks

Résumé

This paper deals with the modelling of complex systems composed by a large number of elements grouped into different functional subsys-tems. The modelling framework is that of the thermostatted kinetic the-ory which consists in a set of nonlinear integro-differential equations. A source of nonlinearity is also the presence of the mathematical thermo-stat that ensures the control of the global energy of the system. Specif-ically this paper is devoted to the derivation of evolution equations for the macroscopic variables (density and momentum) from the underly-ing description at the microscopic scale delivered by the thermostatted kinetic models. To this aim, hyperbolic and parabolic type scalings of the thermostatted kinetic for active particles model are performed and the resulting macroscopic equations are obtained. Finally the asymptotic methods are applied to the relaxation model.
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Dates et versions

hal-01102767 , version 1 (13-01-2015)

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Carlo Bianca, Christian Dogbe. Kinetic models coupled with Gaussian thermostats: macroscopic frameworks. Nonlinearity, 2014, 27 (12), pp.2771-2803. ⟨10.1088/0951-7715/27/12/2771⟩. ⟨hal-01102767⟩
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