Simultaneous uniqueness for multiple parameters identification in a fractional diffusion-wave equation
Simultaneous uniqueness for multiple parameters identification in a fractional diffusion-wave equation
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DOI：
10.3934/ipi.2022019
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发表时间：
2021-03
影响因子：
1.3
通讯作者：
X. Jing;Masahiro Yamamoto
中科院分区：
文献类型：
--
作者：
X. Jing;Masahiro Yamamoto
考虑了导数阶为\开始{document}$ \alpha \in（0，2）$\end{document}的一维时间分数阶扩散波方程的两类同时确定多个参数的反问题.基于对拉普拉斯变换数据极点的分析和变换公式，证明了在没有本征模为零的情况下，从边界测量数据中同时识别多个参数的唯一性，这些参数包括时间导数的阶数、空间变化势、初值和Robin系数.我们的主要结果表明，对于未知阶数\开始{document}$ \alpha $\end{document}变阶数（0，2）包括1，限制到\开始{document}$ \alpha \in都不存在的时间分数阶扩散波模型，四种参数的唯一性同时成立（0，1] $\end{document}或\开始{document}$ \alpha \in（1，2）$\end{document}。此外，对于另一种分数阶扩散波方程，利用非零初值条件下的唯一性结果和Duhamel原理，我们也可以证明多个参数（包括空间变化势和Robin系数）的同时唯一性.
We consider two kinds of inverse problems on determining multiple parameters simultaneously for one-dimensional time-fractional diffusion-wave equations with derivative order \begin{document}$ \alpha \in (0, 2) $\end{document}. Based on the analysis of the poles of Laplace transformed data and a transformation formula, we first prove the uniqueness in identifying multiple parameters, including the order of the derivative in time, a spatially varying potential, initial values, and Robin coefficients simultaneously from boundary measurement data, provided that no eigenmodes are zero. Our main results show that the uniqueness of four kinds of parameters holds simultaneously by such observation for the time-fractional diffusion-wave model where unknown orders \begin{document}$ \alpha $\end{document} vary order (0, 2) including 1, restricted to neither \begin{document}$ \alpha \in (0, 1] $\end{document} nor \begin{document}$ \alpha \in (1, 2) $\end{document}. Furthermore, for another formulation of the fractional diffusion-wave equation with input source term in place of the initial value, we can also prove the simultaneous uniqueness of multiple parameters, including a spatially varying potential and Robin coefficients by means of the uniqueness result in the case of non-zero initial value and Duhamel's principle.