Inverse problem for a nonlocal diffuse optical tomography equation
| Title: | Inverse problem for a nonlocal diffuse optical tomography equation |
|---|---|
| Authors: | Zimmermann, Philipp |
| Source: | Inverse Problems 2023 |
| Publication Year: | 2023 |
| Collection: | Mathematics |
| Subject Terms: | Mathematics - Analysis of PDEs, Primary 35R30, secondary 26A33, 42B37 |
| More Details: | In this article a nonlocal analogue of an inverse problem in diffuse optical tomography is considered. We show that whenever one has given two pairs of diffusion and absorption coefficients $(\gamma_j,q_j)$, $j=1,2$, such that there holds $q_1=q_2$ in the measurement set $W$ and they generate the same DN data, then they are necessarily equal in $\mathbb{R}^n$ and $\Omega$, respectively. Additionally, we show that the condition $q_1|_W=q_2|_W$ is optimal in the sense that without this restriction one can construct two distinct pairs $(\gamma_j,q_j)$, $j=1,2$ generating the same DN data. Comment: 26 pages, 3 figures |
| Document Type: | Working Paper |
| DOI: | 10.1088/1361-6420/ace4ed |
| Access URL: | http://arxiv.org/abs/2302.08610 |
| Accession Number: | edsarx.2302.08610 |
| Database: | arXiv |
Be the first to leave a comment!