Pieraccini, Sandra and Riganti, Riccardo and Belleni-Morante, Aldo:
Numerical Treatment of a Time Dependent Inverse Problem in Photon Transport
Bollettino dell'Unione Matematica Italiana Serie 8 10-B (2007), fasc. n.1, p. 195-211, Unione Matematica Italiana (English)
pdf (518 Kb), djvu (154 Kb). | MR 2310964 | Zbl 1178.45013
Sunto
Si studia un problema inverso unidimensionale per un'equazione integrodiffernziale di una sorgente di differenziale del trasporto di fotoni, e si determinano le proprietà di una sorgente di fotoni ultravioletti immersa in una nube interstellare. Un procedimento iterativo che si basa sulla discretizzazione spazio-temporale del problema diretto, porta alla determinazione della intensità della sorgente e delle sue variazioni al crescere del tempo.
Referenze Bibliografiche
[1] Yu
E. ANIKONOV -
B. A. BUBNOV,
Inverse problems of transport theory,
Sov. Math. Dokl.,
37 (
1988), 497-500. |
MR 947226 |
Zbl 0699.35251[2]
A. BELLENI-MORANTE,
A time dependent inverse problem in photon transport,
World Scientific, Singapore (in press). |
MR 2163962 |
Zbl 1109.82022[3]
A. BELLENI-MORANTE -
R. MONACO -
R. RIGANTI -
F. SALVARANI,
A numerical approach to inverse problems in photon transport inside an intersetllar cloud,
Appl. Math. Comput.,
154 (
2004), 115-126. |
fulltext (doi) |
MR 2066184 |
Zbl 1063.65152[4]
A. BELLENI-MORANTE -
R. MONACO -
F. SALVARANI,
Approximated solutions of photon transport in a time-dependent region,
Transp. Theory Stat. Phys. 30 (
2001), 421-438. |
Zbl 1086.45503[5]
A. BELLENI-MORANTE -
R. RIGANTI,
Inverse problems in photon transport. Part II: features of a source inside an interstellar cloud,
Proceedings of the XII Int. Conference on Waves and Stability in Continuous Media (
R. Monaco,
S. Pennisi,
S. Rionero,
T. Ruggeri, Eds.),
World Scientific, Singapore (
2004), 60-69. |
fulltext (doi) |
MR 2089832 |
Zbl 1066.35106[6]
J. E. DYSON -
D. A. WILLIAMS,
The physics of interstellar medium,
Inst. of Phys. Publ., Bristol,
1997. |
Zbl 1090.85500[7]
V. I. GRYN' -
L. V. NITISHINSKAY,
Inverse three-dimensional problems of the simultaneous determination of the absorption coefficient and the source function for the transport equation,
Comput. Math. Math. Phys.,
32 (
1992), 81-95. |
MR 1164462 |
Zbl 0788.45009[8] G. C. POMRANING, Radiation Hydrodynamics, Prentice Hall Series in Computational Mathematics, Pergamon Press, Oxford, 1973.
[9]
V. A. SHARAFUTDINOV,
The inverse problem of determining a source in a stationary transport equation,
Dokl. Math.,
53 (
1996), 251-253. |
MR 1398761 |
Zbl 0892.58088[10]
C.-W. SHU,
Essentially Non-oscillatory and Weighted Essentially Non-oscillatory Schemes for Hyperbolic Conservation Laws, in
Advanced numerical approximation of nonlinear hyperbolic equations,
Lecture Notes in Mathematics 1697,
Springer,
2000. |
fulltext (doi) |
MR 1728856[11]
P. STEFANOV,
Inverse problems in transport theory, in:
Inside Out: Inverse Problems and Applications (
G. Uhlmann, Ed.),
MSRI Publications,
47,
Cambridge Univ. Press, Cambridge (
2003), 111-131. |
MR 2029679 |
Zbl 1083.45008