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- Title
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.
- Authors
Janno, Jaan
- 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.
- Subjects
HISTORICAL source material; EQUATIONS; INVERSE problems
- Publication
Mathematics (2227-7390), 2023, Vol 11, Issue 2, p456
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math11020456