Inverse source problem for a one-dimensional time-fractional diffusion equation and unique continuation for weak solutions
Inverse source problem for a one-dimensional time-fractional diffusion equation and unique continuation for weak solutions
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DOI：
10.3934/ipi.2022027
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发表时间：
2021-12
影响因子：
1.3
通讯作者：
Zhi-yuan Li;Yikan Liu;Masahiro Yamamoto
中科院分区：
文献类型：
--
作者：
Zhi-yuan Li;Yikan Liu;Masahiro Yamamoto
本文利用最小可能的横向柯西数据，得到了一维时间分数阶扩散方程的反问题解的唯一性。关键成分是唯一的连续性，它适用于弱解决方案。
In this paper, we obtain the sharp uniqueness for an inverse \begin{document}$ x $\end{document}-source problem for a one-dimensional time-fractional diffusion equation with a zeroth-order term by the minimum possible lateral Cauchy data. The key ingredient is the unique continuation which holds for weak solutions.