  The formation and propagation of singularities for Boltzmann equation in
bounded domains has been an important question in numerical studies as well as
in theoretical studies. Consider the nonlinear Boltzmann solution near
Maxwellians under in-flow, diffuse, or bounce-back boundary conditions. We
demonstrate that discontinuity is created at the non-convex part of the grazing
boundary, then propagates only along the forward characteristics inside the
domain before it hits on the boundary again.
