论文标题
在不演示时间内通过数据分数扩散波方程的逆源问题的唯一性
Uniqueness for inverse source problems for fractional diffusion-wave equations by data during not acting time
论文作者
论文摘要
我们考虑具有源项的分数扩散波方程，该方程以时间函数和空间函数的产物形式表示。我们证明，如果源在观测值期间源不起作用，则证明了因数据衰减而确定空间变化因素的唯一性，即通过数据衰减来确定空间变化的因素。如果数据衰减比$ \ left（\ frac {1} {1} {t^p} \ right）$，则我们的主要结果是唯一性衰减，并以\ n $ in \ n $为$ t \ to \ infty $。不是从初始时间开始的日期是现实的，但唯一性一般不知道。证明是基于解决方案产生的函数的分析性和渐近行为。
We consider fractional diffusion-wave equations with source term which is represented in a form of a product of a temporal function and a spatial function. We prove the uniqueness for inveres source problem of determining spatially varying factor by decay of data as the time tends to $\infty$, provided that the source does not work during the observations. Our main result asserts the uniqueness if data decay more rapidly than $\left(\frac{1}{t^p}\right)$ with any $p\in \N$ as $t\to\infty$. Date taken not from the initial time are realistic but the uniqueness was not known in general. The proof is based on the analyticity and the asymptotic behavior of a function generated by the solution.
