Abstract
This paper studies the asymptotic behavior toward rarefaction wave for solutions of the initial value problem to the one-dimensional Broadwell model of the Boltzmann equation. When the Riemann problem for the Euler equation, derived from the Chapman-Enskog expansion, admits the solution of weak rarefaction wave, we also call the corresponding local Maxwellian of the original Broadwell model “rarefaction wave”. Then if the initial data are suitably close to the rarefaction wave at the initial time, the solution is proven to tend toward the rarefaction wave as time goes to infinity. The proof is given by an elementaryL 2 energy method.
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Matsumura, A. Asymptotics toward rarefaction wave of solutions of the Broadwell model of a discrete velocity gas. Japan J. Appl. Math. 4, 489–502 (1987). https://doi.org/10.1007/BF03167816
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DOI: https://doi.org/10.1007/BF03167816