| 概要 |
We study the non-linear half-space problem for the discrete Boltzmann equation (a general discrete velocity model, DVM, with an arbitrary finite number of velocities), where the data for the outgoing particles at the boundary are assigned, possibly linearly depending on the data for the incoming particles, and the solutions are assumed to tend to an assigned Maxwellian at infinity. In the one-dimensional steady case the discrete Boltzmann equation reduces to a system of ODEs. This system is studied based on results by Bobylev and Bernhoff (2003) on the dimensions of the corresponding stable, unstable and center manifolds for singular points (Maxwellians for DVMs). The conditions on the data at the boundary needed for the existence of a unique (in a neighborhood of the assigned Maxwellian) solution of the problem are investigated.
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