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International Journal of Differential Equations
Volume 2016, Article ID 5801728, 8 pages
Research Article

Boundary Layers and Shock Profiles for the Broadwell Model

Department of Mathematics, Karlstad University, 65188 Karlstad, Sweden

Received 26 April 2016; Accepted 19 June 2016

Academic Editor: Giovanni P. Galdi

Copyright © 2016 Niclas Bernhoff. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider the existence of nonlinear boundary layers and the typically nonlinear problem of existence of shock profiles for the Broadwell model, which is a simplified discrete velocity model for the Boltzmann equation. We find explicit expressions for the nonlinear boundary layers and the shock profiles. In spite of the few velocities used for the Broadwell model, the solutions are (at least partly) in qualitatively good agreement with the results for the discrete Boltzmann equation, that is the general discrete velocity model, and the full Boltzmann equation.