On the well-posedness of the Cauchy problem for the equation of radiative transfer with Fresnel 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).…”

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

“…Similar problems for the nonstationary radiation transfer equation are studied in much less detail() (1D case),() (3D case).…”

“…It this paper, we consider the problem describing a nonstationary radiation transfer in multilayered medium with initial data, boundary data and right hand side function from the whole scale of Lebesgue‐type spaces and prove that the problem has a unique solution I . This paper uses the technique of Amosov,() which, in contrast to other studies,() allows to prove the existence of a solution without the additional assumption of existence of a derivative of initial value I 0 . Note that the results of Amosov() in the case under consideration are not applicable, because the verical layers are unbounded in .…”

“…1 In recent years, considerable attention has been paid to the study of boundary value problems for the stationary radiation transfer equation with the conditions of reflection and refraction in different statements and under various constraints on the structure of the domain. [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] Similar problems for the nonstationary radiation transfer equation are studied in much less detail 33,34 (1D case), [35][36][37][38] (3D case).…”