Integrodifferential equations for the two-dimensional transition kernels of invariant imbedding
type: Item
instance of: scholarly article
title: Integrodifferential equations for the two-dimensional transition kernels of invariant imbedding
zbMATH Open document ID: 0870.65140
DOI: 10.1016/0096-3003(95)00331-2
author: O. Diekmann
published in: Applied Mathematics and Computation
publication date: 1997-07-27T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45K05
zbMATH DE Number: 1006537
zbMATH Keywords: invariant imbedding methods
zbMATH Keywords: particle transport theory
zbMATH Keywords: transition operators
zbMATH Keywords: integrodifferential equations
reviewed by: Iulian Coroian
MaRDI profile type: Publication
full work available at URL: 0096-3003(95)00331-2
OpenAlex ID: W1999895507
cites work: An integrodifferential equation for the two-dimensional reflection kernel
cites work: Q3215530
description: scientific article; zbMATH DE number 1006537