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High-order moments conservation in thermostatted kinetic models

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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.

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Acknowledgments

The first author acknowledges the support by the FIRB project RBID08PP3J-Metodi matematici e relativi strumenti per la modellizzazione e la simulazione della formazione di tumori, competizione con il sistema immunitario, e conseguenti suggerimenti terapeutici, Italy.

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Authors and Affiliations

  1. Dipartimento di Scienze Matematiche, Politecnico, 10129 , Torino, Italy

    Carlo Bianca

  2. Dipartimento di Giurisprudenza ed Economia, Università Mediterranea di Reggio Calabria, 89127 , Reggio Calabria, Italy

    Massimiliano Ferrara

  3. Dipartimento di Matematica per le Scienze Economiche e Sociali, Università di Bologna, 40126 , Bologna, Italy

    Luca Guerrini

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  1. Carlo Bianca
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  2. Massimiliano Ferrara
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  3. Luca Guerrini
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Correspondence to Carlo Bianca.

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Bianca, C., Ferrara, M. & Guerrini, L. High-order moments conservation in thermostatted kinetic models. J Glob Optim 58, 389–404 (2014). https://doi.org/10.1007/s10898-013-0045-2

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