Inverse Problem of Identifying a Time-Dependent Source Term in a Fractional Degenerate Semi-Linear Parabolic Equation
This work investigates the inverse problem of identifying a time-dependent source term in a time-fractional semi-linear degenerate parabolic equation using integral measurement data. We establish the unique solvability of the inverse problem within a suitable functional framework. The proof methodol...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-04-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/9/1486 |
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| Summary: | This work investigates the inverse problem of identifying a time-dependent source term in a time-fractional semi-linear degenerate parabolic equation using integral measurement data. We establish the unique solvability of the inverse problem within a suitable functional framework. The proof methodology is based on the Rothe method, where the variational formulation is discretized in time, and a priori estimates for discrete solutions are derived. These estimates are then utilized to demonstrate the convergence of Rothe approximations to a unique weak solution. Additionally, we develop a numerical scheme based on the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>L</mi><mn>1</mn></msup></semantics></math></inline-formula>-Galerkin finite element method, combined with iterative refinement, to reconstruct the unknown source term. The numerical performance of the proposed method is validated through a series of computational experiments, demonstrating its stability and robustness against noisy data. |
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| ISSN: | 2227-7390 |