Generalized Broadwell models for the discrete Boltzmann equation with linear and quadratic terms

A generalization of the Broadwell models for the discrete Boltzmann equation with linear and quadratic terms is investigated. We prove that there exists a time‐global solution to this model in one space‐dimension for locally bounded initial data, using a maximum principle of solutions. The boundedness of solutions is established by analyzing the system of ordinary equations related to the linear term. Copyright © 2000 John Wiley & Sons, Ltd.