Integrodifferential equations for the two-dimensional transition kernels of invariant imbedding
The aim of the paper is the application of invariant imbedding methods for two spatial dimensions to derive a set of integrodifferential equations and related boundary conditions, in the kernels of transmission, left-turn and right-turn transition operators for a two-dimensional particle transport theory problem. The authors model the following problem: given particle fluxes incident at the surfaces of the rectangular region and properties governing the transport process within this region, various transition operators associated with the rectangular region must be determined. The integrodifferential equations along with the auxiliary conditions serve to determine the reflection, transmission, left-turn and right-turn operators. No existence and uniqueness results for the initial problem for the reflection kernel are given. No numerical methods are developed.
scientific article; zbMATH DE number 1006537