Identification of a localized source in an interstellar cloud: an inverse problem

Meri Lisi; Silvia Totaro

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (2005)

  • Volume: 16, Issue: 3, page 203-209
  • ISSN: 1120-6330

Abstract

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We study an inverse problem for photon transport in an interstellar cloud. In particular, we evaluate the position x 0 of a localized source q ⁢ x = q 0 ⁢ δ ⁢ x - x 0 , inside a nebula (for example, a star). We assume that the photon transport phenomenon is one-dimensional. Since a nebula moves slowly in time, the number of photons U inside the cloud changes slowly in time. For this reason, we consider the so-called quasi-static approximation u to the exact solution U . By using semigroup theory, we prove existence and uniqueness of u . Because of some monotonic properties of the operator which describes u as a function of q , the «position» of the source can be evaluated.

How to cite

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Lisi, Meri, and Totaro, Silvia. "Identification of a localized source in an interstellar cloud: an inverse problem." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 16.3 (2005): 203-209. <http://eudml.org/doc/252284>.

@article{Lisi2005,
abstract = {We study an inverse problem for photon transport in an interstellar cloud. In particular, we evaluate the position $x_\{0\}$ of a localized source $q(x) = q_\{0\} \delta(x-x_\{0\})$, inside a nebula (for example, a star). We assume that the photon transport phenomenon is one-dimensional. Since a nebula moves slowly in time, the number of photons $U$ inside the cloud changes slowly in time. For this reason, we consider the so-called quasi-static approximation $u$ to the exact solution $U$. By using semigroup theory, we prove existence and uniqueness of $u$. Because of some monotonic properties of the operator which describes $u$ as a function of $q$, the «position» of the source can be evaluated.},
author = {Lisi, Meri, Totaro, Silvia},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Inverse problems; Quasi-static approximation; Semigroup theory; inverse problems; quasi-static approximation; semigroup theory},
language = {eng},
month = {9},
number = {3},
pages = {203-209},
publisher = {Accademia Nazionale dei Lincei},
title = {Identification of a localized source in an interstellar cloud: an inverse problem},
url = {http://eudml.org/doc/252284},
volume = {16},
year = {2005},
}

TY - JOUR
AU - Lisi, Meri
AU - Totaro, Silvia
TI - Identification of a localized source in an interstellar cloud: an inverse problem
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2005/9//
PB - Accademia Nazionale dei Lincei
VL - 16
IS - 3
SP - 203
EP - 209
AB - We study an inverse problem for photon transport in an interstellar cloud. In particular, we evaluate the position $x_{0}$ of a localized source $q(x) = q_{0} \delta(x-x_{0})$, inside a nebula (for example, a star). We assume that the photon transport phenomenon is one-dimensional. Since a nebula moves slowly in time, the number of photons $U$ inside the cloud changes slowly in time. For this reason, we consider the so-called quasi-static approximation $u$ to the exact solution $U$. By using semigroup theory, we prove existence and uniqueness of $u$. Because of some monotonic properties of the operator which describes $u$ as a function of $q$, the «position» of the source can be evaluated.
LA - eng
KW - Inverse problems; Quasi-static approximation; Semigroup theory; inverse problems; quasi-static approximation; semigroup theory
UR - http://eudml.org/doc/252284
ER -

References

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  1. BELLENI MORANTE, A. - MONACO, R. - SALVARANI, F., Approximated solutions of photon transport in a time dependent region. Transp. Theory Stat. Phys., 30, 2001, 421-438. Zbl1086.45503
  2. CERCIGNANI, C., The Boltzmann Equation and its Applications. Springer-Verlag, New York1987. Zbl0646.76001MR1313028DOI10.1007/978-1-4612-1039-9
  3. DYSON, J.E. - WILLIAMS, D.A., The physics of interstellar medium. Institute of Physics Publishing, Bristol1997. Zbl1090.85500
  4. LARSEN, E.W., Solution of three dimensional inverse transport problems. Transp. Theory Stat. Phys., 17, 1988, 147-167. Zbl0653.45006MR963049DOI10.1080/00411458808230860
  5. LISI, M. - TOTARO, S., Inverse problems related to photon transport in an interstellar cloud. Transp. Theory Stat. Phys., 32, 3-4, 2003, 341-359. Zbl1029.82040MR2014721DOI10.1081/TT-120024767
  6. LISI, M. - TOTARO, S., Photon transport with a localized source in locally convex spaces. Math. Meth. Appl. Sci., 2005, in press. Zbl1107.46050MR2228353DOI10.1002/mma.713
  7. MCCORMICK, N.J., Methods for solving inverse problems for radiation transport, an update. Transp. Theory Stat. Phys., 15, 6-7, 1986, 759-772. Zbl0619.35107MR880891DOI10.1080/00411458608212714
  8. POMRANING, G.C., Radiation hydrodynamics. Pergamon Press, Oxford1973. 
  9. SPITZER, L., Physical Processes in the Interstellar Medium. John Wiley & Sons, Toronto1978. 
  10. ZWEIFEL, P.F., The canonical inverse problem. Transp. Theory Stat. Phys., 28, 1999, 171-179. Zbl0948.65145MR1669041DOI10.1080/00411459908205655

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