A variational technique of mollification applied to backward heat conduction problems
This paper addresses a backward heat conduction problem with fractional Laplacian and time-dependent coefficient in an unbounded domain. The problem models generalized diffusion processes and is well-known to be severely ill-posed. We investigate a simple and powerful variational regularization tech...
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Veröffentlicht in: | Applied mathematics and computation 2023-07, Vol.449, p.127917, Article 127917 |
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | This paper addresses a backward heat conduction problem with fractional Laplacian and time-dependent coefficient in an unbounded domain. The problem models generalized diffusion processes and is well-known to be severely ill-posed. We investigate a simple and powerful variational regularization technique based on mollification. Under classical Sobolev smoothness conditions, we derive order-optimal convergence rates between the exact solution and regularized approximation in the practical case where both the data and the operator are noisy. Moreover, we propose an order-optimal a-posteriori parameter choice rule based on the Morozov principle. Finally, we illustrate the robustness and efficiency of the regularization technique by some numerical examples including image deblurring. |
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ISSN: | 0096-3003 1873-5649 |
DOI: | 10.1016/j.amc.2023.127917 |