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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 1401.92155)] 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:

35A01 Existence problems for PDEs: global existence, local existence, non-existence
35Q82 PDEs in connection with statistical mechanics
82C05 Classical dynamic and nonequilibrium statistical mechanics (general)
35R09 Integro-partial differential equations

Citations:

Zbl 1401.92155
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References:

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