A Convergence Theorem for the Nonequilibrium States in the Discrete Thermostatted Kinetic Theory

Carlo Bianca and Marco Menale
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Carlo Bianca: Laboratoire Quartz EA 7393, École Supérieure d’Ingénieurs en Génie Électrique, Productique et Management Industriel, 95092 Cergy Pontoise CEDEX, France
Marco Menale: Laboratoire Quartz EA 7393, École Supérieure d’Ingénieurs en Génie Électrique, Productique et Management Industriel, 95092 Cergy Pontoise CEDEX, France

Mathematics, 2019, vol. 7, issue 8, 1-13

Abstract: The existence and reaching of nonequilibrium stationary states are important issues that need to be taken into account in the development of mathematical modeling frameworks for far off equilibrium complex systems. The main result of this paper is the rigorous proof that the solution of the discrete thermostatted kinetic model catches the stationary solutions as time goes to infinity. The approach towards nonequilibrium stationary states is ensured by the presence of a dissipative term (thermostat) that counterbalances the action of an external force field. The main result is obtained by employing the Discrete Fourier Transform (DFT).

Keywords: thermostat; nonequilibrium stationary states; discrete Fourier transform; discrete kinetic theory; nonlinearity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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