分野別セミナー

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.