This paper is focused on a nonlinear inverse problem for identifying a space-dependent zeroth-order coefficient in a time-fractional diffusion-wave equation by the measured data on a single boundary point for one-dimensional case. We give the definition of a weak solution and prove its existence for the corresponding direct problem by using the Fourier method. Based on the Gronwall inequality, analytic continuation and the Laplace transformation, we obtain the uniqueness for the inverse zeroth-order coefficient problem under some simple requirements to the Neumann boundary data.

中文翻译：

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从单个边界点测量中识别时间分数扩散波方程中与空间相关的零阶系数的唯一性

本文针对非线性逆问题，通过一维情况下单个边界点上的实测数据来识别时间分数扩散波方程中与空间有关的零阶系数。我们给出了一个弱解的定义，并使用傅里叶方法证明了它对于相应的直接问题的存在。基于Gronwall不等式，解析连续性和Laplace变换，我们在对Neumann边界数据有一些简单要求的情况下，获得了零阶逆系数问题的唯一性。