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High-order moments conservation in thermostatted kinetic models

Author

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  • Carlo Bianca
  • Massimiliano Ferrara
  • Luca Guerrini

Abstract

Recently the thermostatted kinetic framework has been proposed as mathematical model for studying nonequilibrium complex systems constrained to keep constant the total energy. The time evolution of the distribution function of the system is described by a nonlinear partial integro-differential equation with quadratic type nonlinearity coupled with the Gaussian isokinetic thermostat. This paper is concerned with further developments of this thermostatted framework. Specifically the term related to the Gaussian thermostat is adjusted in order to ensure the conservation of even high-order moments of the distribution function. The derived framework that constitutes a new paradigm for the derivation of specific models in the applied sciences, is analytically investigated. The global in time existence and uniqueness of the solution to the relative Cauchy problem is proved. Existence and moments conservation of stationary solutions are also performed. Suitable applications and research perspectives are outlined in the last section of the paper. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Carlo Bianca & Massimiliano Ferrara & Luca Guerrini, 2014. "High-order moments conservation in thermostatted kinetic models," Journal of Global Optimization, Springer, vol. 58(2), pages 389-404, February.
    • Handle: RePEc:spr:jglopt:v:58:y:2014:i:2:p:389-404
    DOI: 10.1007/s10898-013-0045-2
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    References listed on IDEAS

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    Cited by:

    1. Carlo Bianca & Marco Menale, 2022. "On the Existence of Self-Similar Solutions in the Thermostatted Kinetic Theory with Unbounded Activity Domain," Mathematics, MDPI, vol. 10(9), pages 1-14, April.

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