Geodesic
Numerical Treatment of a Time Dependent Inverse Problem in Photon Transport
Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 1, pp. 195-211.

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The time-dependent intensity of a UV -photon source, located inside an interstellar cloud, is determined by formulating and solving an inverse problem for the integro-differential transport equation of photons in a one-dimensional slab. Starting from a discretizazion of the direct problem, an iterative procedure is used to compute the values of the source intensity at increasing values of time, and it is applied in some numerical simulations, whose results are presented and discussed.
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. 
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Pieraccini, Sandra; Riganti, Riccardo; Belleni-Morante, Aldo. Numerical Treatment of a Time Dependent Inverse Problem in Photon Transport. Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 1, pp. 195-211. http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_1_a9/

[1] Yu E. Anikonov - B. A. Bubnov, Inverse problems of transport theory, Sov. Math. Dokl., 37 (1988), 497-500. | MR | Zbl

[2] A. Belleni-Morante, A time dependent inverse problem in photon transport, World Scientific, Singapore (in press). | MR | Zbl

[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. | DOI | MR | Zbl

[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

[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. | DOI | MR | Zbl

[6] J. E. Dyson - D. A. Williams, The physics of interstellar medium, Inst. of Phys. Publ., Bristol, 1997. | Zbl

[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 | Zbl

[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 | Zbl

[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. | DOI | MR

[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 | Zbl