Uniqueness of inverse source problems for time-fractional diffusion equations with singular functions in time
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2022
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914628970217472 |
|---|---|
| author | Liu, Yikan Yamamoto, Masahiro |
| author_facet | Liu, Yikan Yamamoto, Masahiro |
| contents | We consider a fractional diffusion equations of order $α\in(0,1)$ whose source term is singular in time: $(\partial_t^α+A)u(x,t)=μ(t)f(x)$, $(x,t)\inΩ\times(0,T)$, where $μ$ belongs to a Sobolev space of negative order. In inverse source problems of determining $f|_Ω$ by the data $u|_{ω\times(0,T)}$ with a given subdomain $ω\subsetΩ$ or $μ|_{(0,T)}$ by the data $u|_{\{x_0\}\times(0,T)}$ with a given point $x_0\inΩ$, we prove the uniqueness by reducing to the case $μ\in L^2(0,T)$. The key is a transformation of a solution to an initial-boundary value problem with a regular function in time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_04122 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Uniqueness of inverse source problems for time-fractional diffusion equations with singular functions in time Liu, Yikan Yamamoto, Masahiro Analysis of PDEs We consider a fractional diffusion equations of order $α\in(0,1)$ whose source term is singular in time: $(\partial_t^α+A)u(x,t)=μ(t)f(x)$, $(x,t)\inΩ\times(0,T)$, where $μ$ belongs to a Sobolev space of negative order. In inverse source problems of determining $f|_Ω$ by the data $u|_{ω\times(0,T)}$ with a given subdomain $ω\subsetΩ$ or $μ|_{(0,T)}$ by the data $u|_{\{x_0\}\times(0,T)}$ with a given point $x_0\inΩ$, we prove the uniqueness by reducing to the case $μ\in L^2(0,T)$. The key is a transformation of a solution to an initial-boundary value problem with a regular function in time. |
| title | Uniqueness of inverse source problems for time-fractional diffusion equations with singular functions in time |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2209.04122 |