Transport equation and tomography
By: D.S. Anikonov, A.E. Kovtanyuk and I.V. Prokhorov.
Series: Inverse and ill-posed problems series,
Publisher: VSP
Published: 2002
Place of publication: Utrecht; Boston
Language: eng
Number of pages: 207
Subjects: Radiative transfer -- Mathematics.; Transport theory.; Tomography -- Mathematical models.
Notes: Includes bibliographical references (p. [193]-207).
Table of contents: title: Machine generated contents note: Part 1. Direct and inverse problems for the transport equation with energy dependence13; title: 1.1. Derivation of the radiation transport equation13; title: 1.2. Formulation and investigation of the direct problem for the transport equation18; title: 1.3. Continuity of solutions to the direct problem 28; title: 1.4. Determination of the total attenuation coefficient for discontinuous density of the input flux 33; title: 1.5. Description of a source with discontinuous radiation density39; title: 1.6. A boundary value problem with a parameter for the transport equation 44; title: 1.7. Determining the total interaction coefficient by multiple irradiation53; title: 1.8. Providing special boundary conditions for multiple irradiation55; title: 1.9. Testing the algorithms for determining unknown media 65; title: Part 2. The tomography problem in the monoenergetic case 77; title: 2.1. The direct problem for the monoenergetic transport equation77; title: 2.2. Additional restrictions 85; title: 2.3. A formula for the gradient of a solution to the transport equation89; title: 2.4. Auxiliary statements102; title: 2.5. The indicator of heterogeneity in the tomography problem, and the measure of visibility 122; title: 2.6. Invisibility media in tomography 141; title: 2.7. Computerized testing of the indicator of heterogeneity148; title: 2.8. Some contradictions between two mathematical models of transport theory 160; title: 2.9. Comparing two models in transport theory in the plane-parallel case 175; title: 2.10. Prospective investigation 186.