Inverse Coefficient Problem for One-Dimensional Subdiffusion with Data on Disjoint Sets in Time
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_ | 1866929281253244928 |
|---|---|
| author | Cen, Siyu Jin, Bangti Kian, Yavar Soccorsi, Eric Zarouf, Rachid Zhou, Zhi |
| author_facet | Cen, Siyu Jin, Bangti Kian, Yavar Soccorsi, Eric Zarouf, Rachid Zhou, Zhi |
| contents | In this work we investigate an inverse coefficient problem for the one-dimensional subdiffusion model, which involves a Caputo fractional derivative in time. The inverse problem is to determine two coefficients and multiple parameters (the order, and length of the interval) from one pair of lateral Cauchy data. The lateral Cauchy data are given on disjoint sets in time with a single excitation and the measurement is made on a time sequence located outside the support of the excitation. We prove two uniqueness results for different lateral Cauchy data. The analysis is based on the solution representation, analyticity of the observation and a refined version of inverse Sturm-Liouville theory due to Sini [35]. Our results heavily exploit the memory effect of fractional diffusion for the unique recovery of the coefficients in the model. Several numerical experiments are also presented to complement the analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_11599 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Inverse Coefficient Problem for One-Dimensional Subdiffusion with Data on Disjoint Sets in Time Cen, Siyu Jin, Bangti Kian, Yavar Soccorsi, Eric Zarouf, Rachid Zhou, Zhi Analysis of PDEs Numerical Analysis In this work we investigate an inverse coefficient problem for the one-dimensional subdiffusion model, which involves a Caputo fractional derivative in time. The inverse problem is to determine two coefficients and multiple parameters (the order, and length of the interval) from one pair of lateral Cauchy data. The lateral Cauchy data are given on disjoint sets in time with a single excitation and the measurement is made on a time sequence located outside the support of the excitation. We prove two uniqueness results for different lateral Cauchy data. The analysis is based on the solution representation, analyticity of the observation and a refined version of inverse Sturm-Liouville theory due to Sini [35]. Our results heavily exploit the memory effect of fractional diffusion for the unique recovery of the coefficients in the model. Several numerical experiments are also presented to complement the analysis. |
| title | Inverse Coefficient Problem for One-Dimensional Subdiffusion with Data on Disjoint Sets in Time |
| topic | Analysis of PDEs Numerical Analysis |
| url | https://arxiv.org/abs/2403.11599 |