Large time behaviour of homogeneous systems in the continuous thermostatted kinetic theory

Carlo Bianca; Marco Menale

Carlo Bianca Laboratoire Quartz EA 7393, \'{E}cole Sup\'{e}rieure d'Ing\'{e}nieurs en G\'{e}nie \'{E}lectrique, Productique et Management Industriel, 95092 Cergy-Pontoise, France
Marco Menale Laboratoire de Recherche en Eco-innovation Industrielle et Energ\'{e}tique, \'{E}cole Sup\'{e}rieure d'Ing\'{e}nieurs en G\'{e}nie \'{E}lectrique, Productique et Management Industriel, 95092 Cergy-Pontoise, France

Abstract

In the mathematical modeling of a far-from-equilibrium complex system an important target is the understanding of the large time behaviour. This paper focuses on a continuous-homogeneous-conservative mathematical framework coming from the thermostatted kinetic theory recently proposed for the modeling of complex living systems. Specifically by introducing a scaling parameter and letting this parameter going towards zero, the large time behavior of the system is reached, which consists in a nonequilibrium stationary state. The formal proof is obtained in the Lebesgue space $L^1$.