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

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.

Automated summary

This paper introduces a new thermostatted kinetic theory framework for modeling inhomogeneous complex systems, focusing on the role of space and velocity variables. Through nonlinear analysis methods, it establishes the existence and uniqueness of weak solutions to related initial-boundary value problems, using the Galerkin approximation method. Future research directions are outlined in the conclusion section of the paper.