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On the convergence toward nonequilibrium stationary states in thermostatted kinetic models
Author(s) -
Bianca Carlo,
Menale Marco
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5766
Subject(s) - non equilibrium thermodynamics , convergence (economics) , statistical physics , kinetic theory , kinetic energy , fourier transform , mathematics , partial differential equation , classical mechanics , physics , mathematical analysis , theoretical physics , thermodynamics , economics , economic growth
A differential equation‐based framework is suitable for the modeling of nonequilibrium complex systems if its solution is able to reach, as time goes to infinity, the related nonequilibrium steady states. The thermostatted kinetic theory framework has been recently proposed for the modeling of complex systems subjected to an external force field. The present paper is devoted to the mathematical proof of the convergence of the solutions of the thermostatted kinetic framework towards the related nonequilibrium stationary states. The proof of the main result is gained by employing the Fourier transform and distribution theory arguments.