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
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 fac...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/2/456 |
| _version_ | 1797438986619191296 |
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| author | Jaan Janno |
| author_facet | Jaan Janno |
| author_sort | Jaan Janno |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T11:45:17Z |
| format | Article |
| id | doaj.art-35c7e5d3fd13467f8ec3b333ef15ee5b |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T11:45:17Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-35c7e5d3fd13467f8ec3b333ef15ee5b2023-11-30T23:22:28ZengMDPI AGMathematics2227-73902023-01-0111245610.3390/math11020456Inverse 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 SourceJaan Janno0Department of Cybernetics, Tallinn University of Technology, Ehitajate tee 5, 19086 Tallinn, EstoniaIn 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.https://www.mdpi.com/2227-7390/11/2/456inverse problemfractional diffusion-wave equationfinal overdeterminationsource reconstruction |
| spellingShingle | Jaan Janno 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 Mathematics inverse problem fractional diffusion-wave equation final overdetermination source reconstruction |
| 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 |
| title_full | 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 |
| title_fullStr | 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 |
| title_full_unstemmed | 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 |
| title_short | 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 |
| title_sort | 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 |
| topic | inverse problem fractional diffusion-wave equation final overdetermination source reconstruction |
| url | https://www.mdpi.com/2227-7390/11/2/456 |
| work_keys_str_mv | AT jaanjanno inverseproblemtodeterminetwotimedependentsourcefactorsoffractionaldiffusionwaveequationsfromfinaldataandsimultaneousreconstructionoflocationandtimehistoryofapointsource |