A boundary-value problem for the polarized-radiation transfer equation with Fresnel interface conditions for a layered medium

Solvability of the initial-boundary value problem for an integrodifferential equation

“…Inserting the resulting estimate into (20), we see that (13) holds in this case as well. By (13), we deduce from (11) that…”

“…In this case the estimate for f + is rougher than in (13). Thus, we apply finer arguments using the positivity of the operators P λ and E λ .…”

“…Thus, for λ > λ * a solution to (15) exists and is unique. Let us establish (13). In principle, we can estimate the norm of f + in terms of P λ B as…”

“…The concrete form of the matching operator B is determined by the characteristics of radiation and interfaces. The most widespread matching conditions in radiation transfer theory are those corresponding to the continuous "gluing" of the solution [1,2] as well as Fresnel and diffusion type conditions [9][10][11][12][13]. Note that we do not exclude the case of a breeding medium and its boundaries, and thus, do not impose the restrictions Λ ≤ 1 and B ≤ 1 typical for the solvability of the stationary boundary value problem [9][10][11][12][13].…”

“…The articles [9][10][11][12][13] are devoted to studying boundary value problems for the stationary radiation transfer equation with generalized matching conditions at the interface between the media. Continuing the research in this article, we consider the case of nonstationary equation in a medium with plane-parallel geometry.…”