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April  2019, 13(2): 337-351. doi: 10.3934/ipi.2019017

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

 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

Received  April 2018 Revised  August 2018 Published  January 2019

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

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.

Citation: I-Kun Chen, Daisuke Kawagoe. Propagation of boundary-induced discontinuity in stationary radiative transfer and its application to the optical tomography. Inverse Problems & Imaging, 2019, 13 (2) : 337-351. doi: 10.3934/ipi.2019017
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