## On the discrete Boltzmann equation with linear and nonlinear terms

J. Math. Sci. Univ. Tokyo
Vol. 1 (1994), No. 2, Page 277--304.

Yamazaki, Mitsuru
On the discrete Boltzmann equation with linear and nonlinear terms

Abstract:
For the discrete Boltzmann equation with linear and nonlinear terms, we show a boundedness of solutions with an explicit estimate and their asymptotic behavior when the momentum is conserved. Secondly when the Cauchy data are small, we show an exponential decay of solutions, for a model in which the nonlinear terms represent the binary collisions' and also multiple collisions'.

Mathematics Subject Classification (1991): Primary 35Q35; Secondary 82C40, 76P05
Mathematical Reviews Number: MR1317461