For small enough data and domain, the unsteady general planar four-velocity Broadwell system with Dirichlet data has a unique non-negative solution whose first derivatives are bounded except on finitely many planes.
Gatignol, Théorie cinétique d’un gaz à répartition discrète de vitesses
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Existence and uniqueness of classical solution to an initial-boundary value problem for the unsteady general planar Broadwell model with four velocities
For small enough data and domain, the unsteady general planar four-velocity Broadwell system with Dirichlet data has a unique non-negative solution whose first derivatives are bounded except on finitely many planes.