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.
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BibTeX
@misc{sobah2026global,
title = {{Global classical solutions for the general planar Broadwell model with arbitrary velocity orientation: a fixed-point framework}},
author = {Koudzo Togbévi Selom Sobah and Amah Séna d'Almeida},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.08434},
eprint = {2608.08434},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.08434},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Global classical solutions for the general planar Broadwell model with arbitrary velocity orientation: a fixed-point framework
AU - Koudzo Togbévi Selom Sobah
AU - Amah Séna d'Almeida
PY - 2026
DA - 2026/09/06
PB - arXiv
DO - 10.48550/arxiv.2608.08434
UR - https://arxiv.org/abs/2608.08434
AB - 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.
ER -