Initial boundary value problem for the radiative transfer equation with diffusion matching conditions

Initial-boundary value problem for a radiative transfer equation with generalized matching conditions

“…Solvability of the stationary boundary-value problems with the generalized conjugation conditions describing the Fresnel or diffuse reflection and refraction at the interfaces of the media have been investigated in [19][20][21][22][23][24][25][26]. Problems for the non-stationary radiation transfer equations with the generalized matching conjugation conditions in a threedimensional bounded media and in a plane-parallel layered media have been considered in [27][28][29][30][31][32][33][34][35].…”

“…Consider the following integro-differential equation [29][30][31][32]34] (1) 1 v(r) ∂ ∂t + ω · ∇ r + µ(r) I(r, ω, t) = = σ(r) Ω p(r, ω · ω )I(r, ω , t)dω + J(r, ω, t).…”

“…and B d is the operator describing diffuse reflection and refraction [30,32,35] at the interfaces according to Lambert's law:…”