Uniqueness for Inverse Source Problems of Determining a Space-Dependent Source in Time-Fractional Equations with Non-Smooth Solutions
In this contribution, we investigate an inverse source problem for a fractional diffusion and wave equation with the Caputo fractional derivative of the space-dependent variable order. More specifically, we discuss the uniqueness of a solution when reconstructing a space-dependent source from a time...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-10-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/5/4/169 |
| _version_ | 1797504488434565120 |
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| author | Karel Van Bockstal |
| author_facet | Karel Van Bockstal |
| author_sort | Karel Van Bockstal |
| collection | DOAJ |
| description | In this contribution, we investigate an inverse source problem for a fractional diffusion and wave equation with the Caputo fractional derivative of the space-dependent variable order. More specifically, we discuss the uniqueness of a solution when reconstructing a space-dependent source from a time-averaged measurement, or a final in time measurement. Weakly singular solutions are included in the class of admissible solutions. The obtained results are also valid if the order of the fractional derivative is constant. |
| first_indexed | 2024-03-10T04:05:17Z |
| format | Article |
| id | doaj.art-5751a53db3c24bf8b92d3b556ec60338 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T04:05:17Z |
| publishDate | 2021-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-5751a53db3c24bf8b92d3b556ec603382023-11-23T08:23:13ZengMDPI AGFractal and Fractional2504-31102021-10-015416910.3390/fractalfract5040169Uniqueness for Inverse Source Problems of Determining a Space-Dependent Source in Time-Fractional Equations with Non-Smooth SolutionsKarel Van Bockstal0Research Group NaM<sup><i>2</i></sup>, Department of Electronics and Information Systems, Ghent University, Krijgslaan 281, 9000 Ghent, BelgiumIn this contribution, we investigate an inverse source problem for a fractional diffusion and wave equation with the Caputo fractional derivative of the space-dependent variable order. More specifically, we discuss the uniqueness of a solution when reconstructing a space-dependent source from a time-averaged measurement, or a final in time measurement. Weakly singular solutions are included in the class of admissible solutions. The obtained results are also valid if the order of the fractional derivative is constant.https://www.mdpi.com/2504-3110/5/4/169time-fractional diffusion equationnon-autonomousinverse source problemuniqueness |
| spellingShingle | Karel Van Bockstal Uniqueness for Inverse Source Problems of Determining a Space-Dependent Source in Time-Fractional Equations with Non-Smooth Solutions Fractal and Fractional time-fractional diffusion equation non-autonomous inverse source problem uniqueness |
| title | Uniqueness for Inverse Source Problems of Determining a Space-Dependent Source in Time-Fractional Equations with Non-Smooth Solutions |
| title_full | Uniqueness for Inverse Source Problems of Determining a Space-Dependent Source in Time-Fractional Equations with Non-Smooth Solutions |
| title_fullStr | Uniqueness for Inverse Source Problems of Determining a Space-Dependent Source in Time-Fractional Equations with Non-Smooth Solutions |
| title_full_unstemmed | Uniqueness for Inverse Source Problems of Determining a Space-Dependent Source in Time-Fractional Equations with Non-Smooth Solutions |
| title_short | Uniqueness for Inverse Source Problems of Determining a Space-Dependent Source in Time-Fractional Equations with Non-Smooth Solutions |
| title_sort | uniqueness for inverse source problems of determining a space dependent source in time fractional equations with non smooth solutions |
| topic | time-fractional diffusion equation non-autonomous inverse source problem uniqueness |
| url | https://www.mdpi.com/2504-3110/5/4/169 |
| work_keys_str_mv | AT karelvanbockstal uniquenessforinversesourceproblemsofdeterminingaspacedependentsourceintimefractionalequationswithnonsmoothsolutions |