The Boltzmann equation in a bounded domain with specularly reflecting boundaries
Andrej Palczewski · Transport Theory and Statistical Physics · 1992
The paper deals with the stationary Boltzmann equation in a bounded domain Ω. The boundary ∂Ω is assumed to be a convex polyhedron. As a boundary condition we impose specular reflection. The nonlinear Boltzmann equation is considered with an additional source term, and it has been proved that for a sufficiently small source the problem possesses a unique solution in a properly chosen subspace of C(Ω × IR3).