Premium
Relationship Between the Albedo and Scattering Operators for the Boltzmann Equation with Semi‐transparent Boundary Conditions
Author(s) -
Emamirad H.,
Protopopescu V.
Publication year - 1996
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(19960110)19:1<1::aid-mma756>3.0.co;2-j
Subject(s) - scattering , boltzmann equation , mathematics , boundary value problem , boundary (topology) , scattering theory , mathematical analysis , convection–diffusion equation , extension (predicate logic) , albedo (alchemy) , boltzmann constant , physics , quantum mechanics , computer science , art , performance art , art history , programming language
The albedo and scattering operators are central objects in the time‐dependent transport theory. Their mutual relationship has recently been established by Arianfar and Emamirad for the case of transparent boundaries. In this paper, we extend the result to general boundary conditions. To allow for this extension, the scattering theory for a transport‐like equation is generalized to include partially reflecting boundary conditions. The existence of the wave and scattering operators is directly inferred from the properties of the evolution operators that are determined, in turn, by the physics of collisions within and at the boundaries of the scattering domain.