Inverse Problem to Determine Two Time-Dependent Source Factors of Fractional Diffusion-Wave Equations from Final Data and Simultaneous Reconstruction of Location and Time History of a Point Source

Abstract

In this paper, two inverse problems for the fractional diffusion-wave equation that use final data are considered. The first problem consists in the determination of two time-dependent source terms. Uniqueness for this inverse problem is established under an assumption that given space-dependent factors of these terms are “sufficiently different”. The proof uses asymptotical properties of Mittag–Leffler functions. In the second problem, the aim is to reconstruct a location and time history of a point source. The uniqueness for this problem is deduced from the uniqueness theorem for the previous problem in the one-dimensional case.