Onset of Hyperbolic Macroscopic Behavior in Complex Systems Subjected to External Agents

Authors

Carlo Bianca, Laboratoire de Physique Th´eorique de la Mati`ere Condens´ee, Sorbonne Universit´es, UPMC Univ Paris 06, UMR 7600, 75252 Paris cedex 05, France\\ CNRS, UMR 7600 LPTMC, Paris, FranceFollow
Christian Dogbe, Department of Mathematics, Universit´e de Caen, LMNO, CNRS, UMR 6139, 14032 Caen cedex, FranceFollow
Annie Lemarchand, Laboratoire de Physique Th´eorique de la Mati`ere Condens´ee, Sorbonne Universit´es, UPMC Univ Paris 06, UMR 7600, 75252 Paris cedex 05, France\\ CNRS, UMR 7600 LPTMC, Paris, FranceFollow

Author Country (or Countries)

France

Abstract

This paper deals with the derivation of hyperbolic equations from a space inhomogeneous thermostatted kinetic equation which can be proposed for the modeling of complex systems subjected to the external actions at the microscopic and macroscopic scales. The particles of the system are able to perform an activity which is modeled by introducing a specific variable. The derivation of the hyperbolic equations is obtained by performing different scalings into the time and space variables and letting the scaling parameter goes to zero. Applications and future research direction are discussed into the last section of the paper.

Recommended Citation

Bianca, Carlo; Dogbe, Christian; and Lemarchand, Annie (2023) "Onset of Hyperbolic Macroscopic Behavior in Complex Systems Subjected to External Agents," Applied Mathematics & Information Sciences: Vol. 09: Iss. 5, Article 31.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol09/iss5/31