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http://hdl.handle.net/10397/93852
Title: | Reconstruction of a space-time-dependent source in subdiffusion models via a perturbation approach | Authors: | Jin, B Kian, Y Zhou, Z |
Issue Date: | 2021 | Source: | SIAM journal on mathematical analysis, 2021, v. 53, no. 4, p. 4445-4473 | Abstract: | In this article we study two inverse problems of recovering a space-time-dependent source component from the lateral boundary observation in a subdiffusion model. The mathematical model involves a Djrbashian-Caputo fractional derivative of order α ∊ (0, 1) in time, and a second-order elliptic operator with time-dependent coefficients. We establish a well-posedness and a conditional stability result for the inverse problems using a novel perturbation argument and refined regularity estimates of the associated direct problem. Further, we present a numerical algorithm for efficiently and accurately reconstructing the source component, and we provide several two-dimensional numerical results showing the feasibility of the recovery. | Keywords: | Conditional stability Inverse source problem Reconstruction Subdiffusion Time-dependent coefficient |
Publisher: | Society for Industrial and Applied Mathematics | Journal: | SIAM journal on mathematical analysis | ISSN: | 0036-1410 | EISSN: | 1095-7154 | DOI: | 10.1137/21M1397295 | Rights: | © 2021 Society for Industrial and Applied Mathematics The following publication Jin, B., Kian, Y., & Zhou, Z. (2021). Reconstruction of a space-time-dependent source in subdiffusion models via a perturbation approach. SIAM Journal on Mathematical Analysis, 53(4), 4445-4473 is available at https://doi.org/10.1137/21M1397295 |
Appears in Collections: | Journal/Magazine Article |
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21m1397295.pdf | 3.16 MB | Adobe PDF | View/Open |
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