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Existence of stationary solutions in kinetic models with Gaussian thermostats
Author(s) -
Bianca Carlo
Publication year - 2013
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.2722
Subject(s) - thermostat , mathematics , nonlinear system , gaussian , quadratic equation , kinetic energy , field (mathematics) , action (physics) , statistical physics , classical mechanics , thermodynamics , physics , pure mathematics , geometry , quantum mechanics
The thermostatted kinetic framework has been recently proposed in [C. Bianca, Nonlinear Analysis: Real World Applications 13 (2012) 2593‐2608] for the modeling of complex systems in the applied sciences under the action of an external force field that moves out of equilibrium the system. The framework consists in an integro‐differential equation with quadratic nonlinearity coupled with the Gaussian isokinetic thermostat. This paper is concerned with the existence of stationary solutions proof. The main result is gained by fixed point and measure theory arguments. Copyright © 2013 John Wiley & Sons, Ltd.