Diffusion Approximation for Linear Transport with Multiplying Boundary Conditions
V. Protopopescu, L. Thevenot · SIAM Journal on Applied Mathematics · 2005
We consider the diffusion limit of a suitably rescaled model transport equation in a slab with multiplying boundary conditions, as the scaling parameter $\varepsilon$ tends to zero. We show that, for sufficiently smooth data, the solution converges in the L 2 -norm for each t > 0 to the solution of a diffusion equation with Robin boundary conditions corresponding to an incoming flux. The derivation of the diffusive limit is based on an asymptotic expansion, which is rigorously justified.