Nonstationary radiation transfer through a multilayered medium with reflection and refraction conditions

Abstract

We consider an initial‐boundary value problem for the radiation transfer equation with reflection and refraction conditions describing a nonstationary process of the radiation transfer in multilayered semitransparent for radiation medium, consisting of m parallel vertical layers. We establish the existence and uniqueness of a solution for the problem with data from the spaces of Lp type, 1 ≤ p ≤ ∞. We also obtain a priori estimates for the solution and prove an exponential stabilization of the solution as T→∞.

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

“…As relation (33) is also valid for the function f ∈ D, repeating the proof it is easy to verify the existence of the limit functions f + ± ∈ L ∞ (X + ). Passing to the limit in equality (33), we conclude that the functions f ± satisfy equation (31) with Φ = Φ ± . Hence, we have shown the existence of the solution f of equation (31) satisfying estimate (32).…”

“…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].…”