Global classical solutions for the general planar Broadwell model with arbitrary velocity orientation: a fixed-point framework

Abstract

The present work extends a fixed-point framework previously developed for the standard planar four-velocity Broadwell model to the general four-velocity configuration with an arbitrary orientation of the discrete velocities. This provides a non-axis-aligned test of the framework and leads to a global-in-time existence and uniqueness result for classical solutions of the associated initial-boundary value problem in a rectangular domain. Under suitable assumptions on the initial and boundary data, we establish the existence and uniqueness of a global-in-time classical solution. The analysis identifies the geometric and analytic properties of the fixed-point approach that remain valid independently of the orientation of the discrete velocities. The results demonstrate the applicability of the framework to the general planar four-velocity Broadwell model beyond the standard axis-aligned configuration.