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Existence of stationary solutions in kinetic models with Gaussian thermostats. (English) Zbl 1273.35011
Summary: The thermostatted kinetic framework has been recently proposed in [the author, Nonlinear Anal., Real World Appl. 13, No. 6, 2593–2608 (2012; Zbl 06118802)] 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.
MSC:
35A01Existence problems for PDE: global existence, local existence, non-existence
35Q82PDEs in connection with statistical mechanics
82C05Classical dynamic and nonequilibrium statistical mechanics (general)
35R09Integro-partial differential equations