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PreprintCC BY-NC-ND 4.0arXiv

Global existence and uniqueness for the planar four-velocity Broadwell model with arbitrary C1 bounded initial and boundary data in a rectangular domain

  • Koudzo Togbévi Selom Sobah
  • Amah Séna D'Almeida
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Abstract

This paper establishes the global existence of classical solutions to the initial-boundary value problem for the planar four-velocity Broadwell model in a multidimensional setting. While uniqueness was already established in our previous work (which addressed existence under the assumption of sufficiently small, bounded, and C1-regular initial and boundary data), the objective of the present study is to completely lift this size restriction. By extending the previously developed fixed-point framework, we prove that the methodology remains highly effective for arbitrary initial and boundary data. Within this generalized setting, both the solutions and their first-order partial derivatives are shown to be well-defined and to exist globally for all times.

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Cite

BibTeXRIS
BibTeX
@misc{sobah2026global,
  title = {{Global existence and uniqueness for the planar four-velocity Broadwell model with arbitrary $C^1$ bounded initial and boundary data in a rectangular domain}},
  author = {Koudzo Togbévi Selom Sobah and Amah Séna D'Almeida},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.22736},
  eprint = {2609.22736},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.22736},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Global existence and uniqueness for the planar four-velocity Broadwell model with arbitrary C^1 bounded initial and boundary data in a rectangular domain
AU  - Koudzo Togbévi Selom Sobah
AU  - Amah Séna D'Almeida
PY  - 2026
DA  - 2026/09/19
PB  - arXiv
DO  - 10.48550/arxiv.2609.22736
UR  - https://arxiv.org/abs/2609.22736
AB  - This paper establishes the global existence of classical solutions to the initial-boundary value problem for the planar four-velocity Broadwell model in a multidimensional setting. While uniqueness was already established in our previous work (which addressed existence under the assumption of sufficiently small, bounded, and C^1-regular initial and boundary data), the objective of the present study is to completely lift this size restriction. By extending the previously developed fixed-point framework, we prove that the methodology remains highly effective for arbitrary initial and boundary data. Within this generalized setting, both the solutions and their first-order partial derivatives are shown to be well-defined and to exist globally for all times.
ER  -