The Role of Nonconservative Interactions in the Asymptotic Limit of Thermostatted Kinetic Models

Acta Applicandae Mathematicae - Tập 139 - Trang 1-24 - 2014
C. Bianca1,2, C. Dogbe3, A. Lemarchand1,2
1UMR 7600, Laboratoire de Physique Théorique de la Matière Condensée, Sorbonne Universités, UPMC Univ Paris 06, Paris Cedex 05, France
2UMR 7600, LPTMC, CNRS, Paris, France
3Department of Mathematics, LMNO, CNRS, UMR 6139, Université de Caen, Caen Cedex, France

Tóm tắt

This paper is concerned with the asymptotic analysis of space-velocity dependent thermostatted kinetic frameworks which include conservative, nonconservative and stochastic operators. The mathematical frameworks are integro-partial differential equations that can be proposed for the modeling of most phenomena occurring in biological and chemical systems. Specifically the paper focuses on the derivation of macroscopic equations obtained by performing a low-field and a high-field scaling into the thermostatted kinetic framework and considering the related convergence when the scaling parameter goes to zero. In the low-field limit, the macroscopic equations show diffusion with respect to both the space variable and a scalar variable that is introduced for the modeling of the strategy of the particle system. In the high-field limit, the macroscopic equations show hyperbolic behavior. The asymptotic analysis is also generalized to systems decomposed in various functional subsystems.

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