Uniqueness for inverse source problems for fractional diffusion-wave equations by data during not acting time

Abstract

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.