Uniqueness for inverse source problems of determining a space-dependent source in time-fractional equations with non-smooth solutions
- Author
- Karel Van Bockstal (UGent)
- Organization
- Project
- Abstract
- 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.
- Keywords
- Statistics and Probability, Statistical and Nonlinear Physics, Analysis, time-fractional diffusion equation, non-autonomous, inverse source problem, uniqueness, IDENTIFICATION
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8725287
- MLA
- Van Bockstal, Karel. “Uniqueness for Inverse Source Problems of Determining a Space-Dependent Source in Time-Fractional Equations with Non-Smooth Solutions.” FRACTAL AND FRACTIONAL, vol. 5, no. 4, 2021, doi:10.3390/fractalfract5040169.
- APA
- Van Bockstal, K. (2021). Uniqueness for inverse source problems of determining a space-dependent source in time-fractional equations with non-smooth solutions. FRACTAL AND FRACTIONAL, 5(4). https://doi.org/10.3390/fractalfract5040169
- Chicago author-date
- Van Bockstal, Karel. 2021. “Uniqueness for Inverse Source Problems of Determining a Space-Dependent Source in Time-Fractional Equations with Non-Smooth Solutions.” FRACTAL AND FRACTIONAL 5 (4). https://doi.org/10.3390/fractalfract5040169.
- Chicago author-date (all authors)
- Van Bockstal, Karel. 2021. “Uniqueness for Inverse Source Problems of Determining a Space-Dependent Source in Time-Fractional Equations with Non-Smooth Solutions.” FRACTAL AND FRACTIONAL 5 (4). doi:10.3390/fractalfract5040169.
- Vancouver
- 1.Van Bockstal K. Uniqueness for inverse source problems of determining a space-dependent source in time-fractional equations with non-smooth solutions. FRACTAL AND FRACTIONAL. 2021;5(4).
- IEEE
- [1]K. Van Bockstal, “Uniqueness for inverse source problems of determining a space-dependent source in time-fractional equations with non-smooth solutions,” FRACTAL AND FRACTIONAL, vol. 5, no. 4, 2021.
@article{8725287,
abstract = {{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.}},
articleno = {{169}},
author = {{Van Bockstal, Karel}},
issn = {{2504-3110}},
journal = {{FRACTAL AND FRACTIONAL}},
keywords = {{Statistics and Probability,Statistical and Nonlinear Physics,Analysis,time-fractional diffusion equation,non-autonomous,inverse source problem,uniqueness,IDENTIFICATION}},
language = {{eng}},
number = {{4}},
pages = {{11}},
title = {{Uniqueness for inverse source problems of determining a space-dependent source in time-fractional equations with non-smooth solutions}},
url = {{http://doi.org/10.3390/fractalfract5040169}},
volume = {{5}},
year = {{2021}},
}
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