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

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 $L^1$.