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Existence and uniqueness of the weak solution for a space–velocity thermostatted kinetic theory framework

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Abstract

This paper analyzes a new thermostatted kinetic theory framework for the modeling of an inhomogeneous complex system. Specifically, the role of the space and velocity variables is taken into account. The mathematical analysis refers to the existence and uniqueness of the weak solution of a related initial-boundary value problem. The main result is gained by employing methods of nonlinear analysis and in particular the Galerkin approximation method. Future research directions are outlined in the last section of the paper.

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Authors and Affiliations

  1. Laboratoire Quartz EA 7393, École Supérieure d’Ingénieurs en Génie Électrique, Productique et Management Industriel, 13 Boulevard de l’Hautil, 95092, Cergy Pontoise Cedex, France

    Carlo Bianca & Marco Menale

  2. Laboratoire de Recherche en Eco-innovation Industrielle et Energétique, École Supérieure d’Ingénieurs en Génie Électrique, Productique et Management Industriel, 13 Boulevard de l’Hautil, 95092, Cergy Pontoise Cedex, France

    Carlo Bianca

  3. Dipartimento di Matematica e Fisica, Università degli Studi della Campania “L. Vanvitelli”, Viale Lincoln 5, 81100, Caserta, Italy

    Marco Menale

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  1. Carlo Bianca
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Correspondence to Carlo Bianca.

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Bianca, C., Menale, M. Existence and uniqueness of the weak solution for a space–velocity thermostatted kinetic theory framework. Eur. Phys. J. Plus 136, 243 (2021). https://doi.org/10.1140/epjp/s13360-021-01233-1

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