Boundary value problem of radiation transfer in an inhomogeneous medium with reflection conditions on the boundary

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

“…Neglecting the effects of this kind leads to the traditional matching conditions such as continuous solution gluing or shot [2,6]. 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].…”

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

“…The boundary value problems with reflection and refraction conditions are much more difficult than the problems with the conditions of the type of continuous gluing of solutions or “shooting conditions.” Some problems with conditions taking into account reflection on the interface between media were treated in Germogenova. () From the mathematical point of view, problems for the equation of radiation transfer with the reflection and refraction conditions in accordance with the Fresnel laws were first studied in the papers,() which were initiated by applications to tomography…”

“…Some problems with conditions taking into account reflection on the interface between media were treated in Germogenova. 14,16 From the mathematical point of view, problems for the equation of radiation transfer with the reflection and refraction conditions in accordance with the Fresnel laws were first studied in the papers, 17,18 which were initiated by applications to tomography. 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.…”

“…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).…”

An extremum problem for the radiation transfer equation

“…In the present paper the problem of interest is examined as an extremum problem for the stationary monochromatic transfer equation with generalized matching conditions [5][6][7] at the interfaces between the media. The matching condition describes the Snell refraction and mirror reflection of radiation at an interface [1,8].…”