Asymptotic Theory of the Linear Transport Equation for Small Mean Free Paths. II
Edward W. Larsen · SIAM Journal on Applied Mathematics · 1977
The asymptotic analysis of the linear transport equation, begun in a previous paper (E. W. Larsen and J. D’Arruda, Asymptotic theory of the linear transport equationfor small mean free paths. I., Phys. Rev. A, 13 (1976), pp. 1933–1939) is here completed. We construct in the present paper initial and boundary layer solutions of the linear transport equation and combine these with the interior solution, which depends on a diffusion equation which was constructed in the earlier paper, to obtain asymptotic solutions to general initial-boundary value problems. In so doing, we derive initial and boundary conditions for the diffusion equation. We consider boundaries which absorb, trap, and reflect particles, with very general laws of reflection.