Geodesic
The asymptotic limit of an integro-differential equation modelling complex systems
Izvestiya. Mathematics , Tome 78 (2014) no. 6, pp. 1105-1119

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This paper is devoted to the asymptotic analysis of a mathematical framework that has recently been proposed for modelling complex systems in the applied sciences under the action of an external force field. This framework consists in an integro-differential kinetic equation coupled with a Gaussian isokinetic thermostat. The asymptotic limit obtained here using low-field scaling shows the emergence of diffusive behaviour on a macroscopic scale.
Keywords: integro-differential equation, low-field limit, velocity-jump process, kinetic theory.
Mots-clés : active particles 
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     title = {The asymptotic limit of an integro-differential equation modelling complex systems},
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C. Bianca; M. Ferrara; L. Guerrini. The asymptotic limit of an integro-differential equation modelling complex systems. Izvestiya. Mathematics , Tome 78 (2014) no. 6, pp. 1105-1119. http://geodesic.mathdoc.fr/item/IM2_2014_78_6_a3/