Propagation of boundary-induced discontinuity in stationary radiative transfer and its application to the optical tomography

I-Kun Chen; Daisuke Kawagoe

doi:10.3934/ipi.2019017

Article Contents

2019, Volume 13, Issue 2: 337-351. Doi: 10.3934/ipi.2019017

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Propagation of boundary-induced discontinuity in stationary radiative transfer and its application to the optical tomography

I-Kun Chen^1, and
Daisuke Kawagoe^2, ,

1.
Institute of Applied Mathematical Sciences, National Taiwan University, No. 1, Sec. 4, Roosevelt Rd., Taipei 10617, Taiwan
2.
Institute of Applied Mathematics, Inha University, 100 Inha-ro, Nam-gu, Incheon, 22212, Republic of Korea

^* Corresponding author
^* Corresponding author

Received: March 31, 2018

Revised: July 31, 2018

Published: March 2019

The first author was supported in part by JSPS KAKENHI grant number 15K17572.

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Abstract

We consider a boundary value problem of the stationary transport equation with the incoming boundary condition in two or three dimensional bounded convex domains. We discuss discontinuity of the solution to the boundary value problem arising from discontinuous incoming boundary data, which we call the boundary-induced discontinuity. In particular, we give two kinds of sufficient conditions on the incoming boundary data for the boundary-induced discontinuity. We propose a method to reconstruct the attenuation coefficient from jumps in boundary measurements.

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Mathematics Subject Classification: Primary: 35R09; Secondary: 35R30, 35Q60.

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References

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