论文标题
时间分数演化方程的逆移动源问题：确定概况
Inverse moving source problem for time-fractional evolution equations: Determination of profiles
论文作者
论文摘要
本文涉及两个逆问题，这些问题在确定具有导数顺序的移动源概况函数$α\ in（0,2] $中的时间。 $ 1 <α\ le2 $，在第二个问题中，假定移动源的轨道是已知的，我们以无限观察时间为代价来考虑完整的横向数据。
This article is concerned with two inverse problems on determining moving source profile functions in evolution equations with a derivative order $α\in(0,2]$ 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 $0<α\le1$ and $1<α\le2$, 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.
