Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.02421 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909965675921408 |
|---|---|
| author | Kong, Lingzheng Deng, Youjun Zhu, Liyan |
| author_facet | Kong, Lingzheng Deng, Youjun Zhu, Liyan |
| contents | In this paper, we study the recovery of multi-layer structures in inverse conductivity problem by using one measurement. First, we define the concept of Generalized Polarization Tensors (GPTs) for multi-layered medium and show some important properties of the proposed GPTs. With the help of GPTs, we present the perturbation formula for general multi-layered medium. Then we derive the perturbed electric potential for multi-layer concentric disks structure in terms of the so-called generalized polarization matrix, whose dimension is the same as the number of the layers. By delicate analysis, we derive an algebraic identity involving the geometric and material configurations of multi-layer concentric disks. This enables us to reconstruct the multi-layer structures by using only one partial-order measurement. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_02421 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Inverse conductivity problem with one measurement: Uniqueness of multi-layer structures Kong, Lingzheng Deng, Youjun Zhu, Liyan Analysis of PDEs 31A25, 35J05, 86A20 In this paper, we study the recovery of multi-layer structures in inverse conductivity problem by using one measurement. First, we define the concept of Generalized Polarization Tensors (GPTs) for multi-layered medium and show some important properties of the proposed GPTs. With the help of GPTs, we present the perturbation formula for general multi-layered medium. Then we derive the perturbed electric potential for multi-layer concentric disks structure in terms of the so-called generalized polarization matrix, whose dimension is the same as the number of the layers. By delicate analysis, we derive an algebraic identity involving the geometric and material configurations of multi-layer concentric disks. This enables us to reconstruct the multi-layer structures by using only one partial-order measurement. |
| title | Inverse conductivity problem with one measurement: Uniqueness of multi-layer structures |
| topic | Analysis of PDEs 31A25, 35J05, 86A20 |
| url | https://arxiv.org/abs/2312.02421 |