A variational technique of mollification applied to backward heat conduction problems

Walter C. Simo Tao Lee

Applied Mathematics and Computation, 2023, vol. 449, issue C

Abstract: 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.

Keywords: Backward heat problems; Mollification; Regularization; Order-optimal rates; Error estimates; Parameter choice rule; Diffusion process (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:449:y:2023:i:c:s0096300323000863

DOI: 10.1016/j.amc.2023.127917

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