Inverse coefficient problems for the heat equation with fractional Laplacian
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910456922243072 |
|---|---|
| author | Mamanazarov, Azizbek Suragan, Durvudkhan |
| author_facet | Mamanazarov, Azizbek Suragan, Durvudkhan |
| contents | In the present paper we study inverse problems related to determining the time-dependent coefficient and unknown source function of fractional heat equations. Our approach shows that having just one set of data at an observation point ensures the existence of a weak solution for the inverse problem. Furthermore, if there is an additional datum at the observation point, it leads to a specific formula for the time-dependent source coefficient. Moreover, we investigate inverse problems involving non-local data and recovering the space-dependent source function of the fractional heat equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_13338 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Inverse coefficient problems for the heat equation with fractional Laplacian Mamanazarov, Azizbek Suragan, Durvudkhan Analysis of PDEs 35R30, 35K05, 35R11 In the present paper we study inverse problems related to determining the time-dependent coefficient and unknown source function of fractional heat equations. Our approach shows that having just one set of data at an observation point ensures the existence of a weak solution for the inverse problem. Furthermore, if there is an additional datum at the observation point, it leads to a specific formula for the time-dependent source coefficient. Moreover, we investigate inverse problems involving non-local data and recovering the space-dependent source function of the fractional heat equation. |
| title | Inverse coefficient problems for the heat equation with fractional Laplacian |
| topic | Analysis of PDEs 35R30, 35K05, 35R11 |
| url | https://arxiv.org/abs/2405.13338 |