The structure of the fundamental solution of the time-independent transport equation
type: Item
instance of: scholarly article
title: The structure of the fundamental solution of the time-independent transport equation
zbMATH Open document ID: 0921.35003
author: Anatoly N. Bondarenko
published in: Journal of Mathematical Analysis and Applications
publication date: 1999-10-07T00:00:00Z
review text: The goal of the author is to give a precise representation of the fundamental solution of the time-independent one-speed transport equation. In the representation there appear different terms which describe the singularities of the fundamental solution. The representation is obtained by studying a corresponding integral equation and constructing the solution by a Neumann series. The singular terms contain some information about the medium. The author announces that these information can be used for solving ``inverse problems'' for the transport equation, e.g., for solving the \(X\)-ray tomography in scattering media problem.
Mathematics Subject Classification ID: 35A08
Mathematics Subject Classification ID: 35A20
Mathematics Subject Classification ID: 45B05
zbMATH DE Number: 1217021
zbMATH Keywords: \(X\)-ray tomography in scattering media problem
zbMATH Keywords: singularities of the fundamental solution
zbMATH Keywords: Neumann series
reviewed by: Michael Reissig
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5842
OpenAlex ID: W2045684213
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DOI: 10.1006/JMAA.1997.5842
description: scientific article; zbMATH DE number 1217021