https://doi.org/10.1140/epjp/s13360-021-01233-1
Regular Article
Existence and uniqueness of the weak solution for a space–velocity thermostatted kinetic theory framework
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
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
3
Dipartimento di Matematica e Fisica, Università degli Studi della Campania “L. Vanvitelli”, Viale Lincoln 5, 81100, Caserta, Italy
Received:
5
January
2021
Accepted:
13
February
2021
Published online:
22
February
2021
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.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021
