Inverse moving source problem for time-fractional evolution equations: determination of profiles
Inverse moving source problem for time-fractional evolution equations: determination of profiles
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DOI：
10.1088/1361-6420/ac0c20
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发表时间：
2020-02
期刊：
影响因子：
2.1
通讯作者：
Yikan Liu;G. Hu;Masahiro Yamamoto
中科院分区：
文献类型：
--
作者：
Yikan Liu;G. Hu;Masahiro Yamamoto
本文讨论了在时间上导数阶数为α ∈（0，2]的发展方程中确定移动源剖面函数的两个反问题。在第一个问题中，假设源沿沿着已知直线运动，并适当地选择有限时间内的部分内部观测数据。将问题归结为初始值的确定，我们证明了当0 < α <$1和1 < α <$2时，一个和两个运动源剖面的唯一确定性。在第二个问题中，假设移动源的轨道已知，并且我们考虑完整的横向柯西数据。以观测时间为无限长为代价，通过构造检验函数，证明了一个运动源剖面的唯一确定性。
This article is concerned with two inverse problems on determining moving source profile functions in evolution equations with a derivative order α ∈ (0, 2] in time. In the first problem, the sources are supposed to move along known straight lines, and we suitably choose partial interior observation data in finite time. Reducing the problems to the determination of initial values, we prove the unique determination of one and two moving source profiles for 0 < α ⩽ 1 and 1 < α ⩽ 2, respectively. In the second problem, the orbits of moving sources are assumed to be known, and we consider the full lateral Cauchy data. At the cost of infinite observation time, we prove the unique determination of one moving source profile by constructing test functions.