Point Source Identification in Subdiffusion from A Posteriori Internal Measurement
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913607624687616 |
|---|---|
| author | Huang, Kuang Jin, Bangti Kian, Yavar Sadaka, Georges Zhou, Zhi |
| author_facet | Huang, Kuang Jin, Bangti Kian, Yavar Sadaka, Georges Zhou, Zhi |
| contents | In this work we investigate an inverse problem of recovering point sources and their time-dependent strengths from {a posteriori} partial internal measurements in a subdiffusion model which involves a Caputo fractional derivative in time and a general second-order elliptic operator in space. We establish the well-posedness of the direct problem in the sense of transposition and improved local regularity. Using classical unique continuation of the subdiffusion model and improved local solution regularity, we prove the uniqueness of simultaneously recovering the locations of point sources, time-dependent strengths and initial condition for both one- and multi-dimensional cases. Moreover, in the one-dimensional case, the elliptic operator can have time-dependent coefficients. These results extend existing studies on point source identification for parabolic type problems. Additionally we present several numerical experiments to show the feasibility of numerical reconstruction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_08220 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Point Source Identification in Subdiffusion from A Posteriori Internal Measurement Huang, Kuang Jin, Bangti Kian, Yavar Sadaka, Georges Zhou, Zhi Analysis of PDEs Numerical Analysis In this work we investigate an inverse problem of recovering point sources and their time-dependent strengths from {a posteriori} partial internal measurements in a subdiffusion model which involves a Caputo fractional derivative in time and a general second-order elliptic operator in space. We establish the well-posedness of the direct problem in the sense of transposition and improved local regularity. Using classical unique continuation of the subdiffusion model and improved local solution regularity, we prove the uniqueness of simultaneously recovering the locations of point sources, time-dependent strengths and initial condition for both one- and multi-dimensional cases. Moreover, in the one-dimensional case, the elliptic operator can have time-dependent coefficients. These results extend existing studies on point source identification for parabolic type problems. Additionally we present several numerical experiments to show the feasibility of numerical reconstruction. |
| title | Point Source Identification in Subdiffusion from A Posteriori Internal Measurement |
| topic | Analysis of PDEs Numerical Analysis |
| url | https://arxiv.org/abs/2412.08220 |