Estimates for solutions to the transport equation under the perturbation of its attenuation and scattering terms

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Published: Jun 30, 2012
DOI: https://doi.org/10.5556/j.tkjm.43.2012.1018
Keywords:
transport equation stability estimate for perturbation albedo operator optical tomography

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Daiki Tanaka
Graduate School of Informatics, Kyoto University, Yoshida-Honmachi, Kyoto, 606-8501, Japan.
Nobuyuki Higashimori
Graduate School of Economics, Hitotsubashi University, Kunitachishi-Naka 2-1, Tokyo, 186-8601, Japan.
Yuusuke Iso
Graduate School of Informatics, Kyoto University, Yoshida-Honmachi, Kyoto, 606-8501, Japan.

Abstract

The aim of the paper is to give $L^p$-estimates for the weak solution to the transport equation with $L^\infty$-perturbation both of the attenuation coefficient and of the scattering kernel. We try to clarify the constants in our estimates, and we show the estimates by a direct calculation. We introduce the albedo operator for the solutions, and we show stability of perturbed albedo operators.

Article Details

How to Cite
Tanaka, D., Higashimori, N., & Iso, Y. (2012). Estimates for solutions to the transport equation under the perturbation of its attenuation and scattering terms. Tamkang Journal of Mathematics, 43(2), 313–320. https://doi.org/10.5556/j.tkjm.43.2012.1018
Issue
Vol. 43 No. 2 (2012)
Section
Papers

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