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A family of discrete velocity models is proposed for the study of particle coagulation and fragmentation in gases. Patterned after the Broadwell model, the models allow inelastic collisions to occur, as well as elastic collisions. The models generate systems of highly coupled semilinear hyperbolic equations which approximate the Boltzmann equation. With the aid of the powerful computer algebra systems Mathematica and Maple, we find an exact four-parameter solution to the simplest model.
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