Asymptotic behavior of one-dimensional discrete-velocity models in a slab
From the discrete velocity models of Boltzmann equation, as introduced by \textit{R. Illner} and \textit{T. Platkowski} [SIAM Rev. 30, 213-255 (1988; Zbl 0668.76087)] and with the notations and the pattern of discussions of \textit{S. Kawashima} [Nonlin. Anal. Theory Methods Appl. 17, 577-597 (1991; Zbl 0763.35075)], some results are obtained on the asymptotic behaviour of the global solution of the initial-boundary value problems in one- dimensional slab \(0 < x < 1\) with general stochastic boundary conditions at \(x = 0\) and \(x = 1\). With the assumption of homogeneity in \(y\)- and \(z\)-spatial directions, the problems discussed are reduced to one- dimensional problems. After a brief discussion of Kawashima's theorems, some results are sharpened. At the end the authors consider the case when collision term is absent.
scientific article; zbMATH DE number 754020
scientific article