Inverse coefficient problem for one-dimensional evolution equation vanishing initial condition
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909330852282368 |
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| author | Y, Oleg Imanuvilov Yamamoto, Masahiro |
| author_facet | Y, Oleg Imanuvilov Yamamoto, Masahiro |
| contents | We consider an inverse problem of determining a coefficient $p(x)$ of an evolution equation $σ\ppp_tu = a(x)\ppp_x^2u - p(x)u$ for $0<x<\ell$ and $0<t<T$, where $σ\in \C \setminus \{0\}$, $\ell>0$ and $T>0$ are arbitrarily given. Our main result is the uniqueness: by assuming that the zeros of initial value $b(x):= u(0,x)$ on $[0, \ell]$ is a finite set and each zero is of order one at most, if two solutions have the same Cauchy data at $x=0$ over $(0,T)$ and the same initial value $b(x)$, then the coefficient $p(x)$ is uniquely determined on $[0,\ell]$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_20321 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Inverse coefficient problem for one-dimensional evolution equation vanishing initial condition Y, Oleg Imanuvilov Yamamoto, Masahiro Analysis of PDEs 35 We consider an inverse problem of determining a coefficient $p(x)$ of an evolution equation $σ\ppp_tu = a(x)\ppp_x^2u - p(x)u$ for $0<x<\ell$ and $0<t<T$, where $σ\in \C \setminus \{0\}$, $\ell>0$ and $T>0$ are arbitrarily given. Our main result is the uniqueness: by assuming that the zeros of initial value $b(x):= u(0,x)$ on $[0, \ell]$ is a finite set and each zero is of order one at most, if two solutions have the same Cauchy data at $x=0$ over $(0,T)$ and the same initial value $b(x)$, then the coefficient $p(x)$ is uniquely determined on $[0,\ell]$. |
| title | Inverse coefficient problem for one-dimensional evolution equation vanishing initial condition |
| topic | Analysis of PDEs 35 |
| url | https://arxiv.org/abs/2409.20321 |