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On the Existence of Self-Similar Solutions in the Thermostatted Kinetic Theory with Unbounded Activity Domain

Author

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  • Carlo Bianca

    (Laboratoire Quartz EA 7393, École Supérieure d’Ingénieurs en Génie Électrique, Productique et Management Industriel, 13 Boulevard de l’Hautil, 95092 Cergy Pontoise, France
    Laboratoire de Recherche en Eco-Innovation Industrielle et Energétique, École Supérieure d’Ingénieurs en Génie Électrique, Productique et Management Industriel, 95092 Cergy Pontoise, France)

  • Marco Menale

    (Dipartimento di Matematica e Fisica, Università degli Studi della Campania “L. Vanvitelli", Viale Lincoln 5, I-81100 Caserta, Italy)

Abstract

This paper is devoted to the mathematical analysis of a spatially homogeneous thermostatted kinetic theory framework with an unbounded activity domain. The framework consists of a partial integro-differential equation with quadratic nonlinearity where the domain of the activity variable is the whole real line. Specifically the mathematical analysis refers firstly to the existence and uniqueness of the solution for the related initial boundary value problem; Secondly the investigations are addressed to the existence of a class of self-similar solutions by employing the Fourier transform method. In particular the main result is obtained for a nonconstant interaction rate and a nonconstant force field. Conclusions and perspectives are discussed in the last section of the paper.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1407-:d:799877
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    References listed on IDEAS

    as
    1. 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.
    2. Bruno Carbonaro & Marco Menale, 2019. "Dependence on the Initial Data for the Continuous Thermostatted Framework," Mathematics, MDPI, vol. 7(7), pages 1-11, July.
    3. Tailong Li & Ping Chen & Jian Xie, 2013. "Self-Similar Solutions of the Compressible Flow in One-Space Dimension," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-5, October.
    4. Carlo Bianca & Caterina Mogno, 2018. "Modelling pedestrian dynamics into a metro station by thermostatted kinetic theory methods," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 24(2), pages 207-235, March.
    Full references (including those not matched with items on IDEAS)

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