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Volume 6, Issue 4
An Inverse Problem of Determining Coefficients in a One-Dimensional Radiative Transport Equation

Nobuyuki Higashimori

DOI: 10.4208/aamm.2014.4.s3

Adv. Appl. Math. Mech., 6 (2014), pp. 515-522.

Published online: 2014-06

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  • Abstract

We consider an inverse problem of determining unknown coefficients for a one-dimensional analogue of radiative transport equation. We show that some combination of the unknown coefficients can be uniquely determined by giving pulse-like inputs at the boundary and observing the corresponding outputs. Our result can be applied for determination of absorption and scattering properties of an optically turbid medium if the radiative transport equation is appropriate for describing the propagation of light in the medium.

  • Keywords

Inverse problem, radiative transport equation, first-order hyperbolic system, optical tomography.

  • AMS Subject Headings

35R30, 35L50, 35Q99, 62P10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-6-515, author = {Higashimori , Nobuyuki}, title = {An Inverse Problem of Determining Coefficients in a One-Dimensional Radiative Transport Equation}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2014}, volume = {6}, number = {4}, pages = {515--522}, abstract = {

We consider an inverse problem of determining unknown coefficients for a one-dimensional analogue of radiative transport equation. We show that some combination of the unknown coefficients can be uniquely determined by giving pulse-like inputs at the boundary and observing the corresponding outputs. Our result can be applied for determination of absorption and scattering properties of an optically turbid medium if the radiative transport equation is appropriate for describing the propagation of light in the medium.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2014.4.s3}, url = {http://global-sci.org/intro/article_detail/aamm/32.html} }
TY - JOUR T1 - An Inverse Problem of Determining Coefficients in a One-Dimensional Radiative Transport Equation AU - Higashimori , Nobuyuki JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 515 EP - 522 PY - 2014 DA - 2014/06 SN - 6 DO - http://doi.org/10.4208/aamm.2014.4.s3 UR - https://global-sci.org/intro/article_detail/aamm/32.html KW - Inverse problem, radiative transport equation, first-order hyperbolic system, optical tomography. AB -

We consider an inverse problem of determining unknown coefficients for a one-dimensional analogue of radiative transport equation. We show that some combination of the unknown coefficients can be uniquely determined by giving pulse-like inputs at the boundary and observing the corresponding outputs. Our result can be applied for determination of absorption and scattering properties of an optically turbid medium if the radiative transport equation is appropriate for describing the propagation of light in the medium.

Nobuyuki Higashimori. (1970). An Inverse Problem of Determining Coefficients in a One-Dimensional Radiative Transport Equation. Advances in Applied Mathematics and Mechanics. 6 (4). 515-522. doi:10.4208/aamm.2014.4.s3
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