Geodesic
On the Structure of the Continuity Set of the Solution to a Boundary-Value Problem for the Radiation Transfer Equation
Matematičeskie zametki, Tome 86 (2009) no. 2, pp. 256-272

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we study the continuity properties of the solution to a boundary-value problem for the radiation transfer equation with generalized conjugation conditions at the interface of media. We establish the solvability of the boundary-value problem and obtain estimates of the maximum principle type. It is shown that the Fresnel component in the conjugation operator significantly complicates the structure of the set on which the solution of the boundary-value problem is continuous.
Keywords: radiation transfer equation, boundary-value problem, conjugation operator, Fresnel reflection, Snell's law, index of refraction.
Mots-clés : diffuse reflection, reflection indicatrix 
@article{MZM_2009_86_2_a8,
     author = {I. V. Prokhorov},
     title = {On the {Structure} of the {Continuity} {Set} of the {Solution} to a {Boundary-Value} {Problem} for the {Radiation} {Transfer} {Equation}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {256--272},
     publisher = {mathdoc},
     volume = {86},
     number = {2},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2009_86_2_a8/}
}
TY  - JOUR
AU  - I. V. Prokhorov
TI  - On the Structure of the Continuity Set of the Solution to a Boundary-Value Problem for the Radiation Transfer Equation
JO  - Matematičeskie zametki
PY  - 2009
SP  - 256
EP  - 272
VL  - 86
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2009_86_2_a8/
LA  - ru
ID  - MZM_2009_86_2_a8
ER  - 
%0 Journal Article
%A I. V. Prokhorov
%T On the Structure of the Continuity Set of the Solution to a Boundary-Value Problem for the Radiation Transfer Equation
%J Matematičeskie zametki
%D 2009
%P 256-272
%V 86
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2009_86_2_a8/
%G ru
%F MZM_2009_86_2_a8
I. V. Prokhorov. On the Structure of the Continuity Set of the Solution to a Boundary-Value Problem for the Radiation Transfer Equation. Matematičeskie zametki, Tome 86 (2009) no. 2, pp. 256-272. http://geodesic.mathdoc.fr/item/MZM_2009_86_2_a8/