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A variational technique of mollification applied to backward heat conduction problems

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  • Simo Tao Lee, Walter 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.

Suggested Citation

  • Simo Tao Lee, Walter C., 2023. "A variational technique of mollification applied to backward heat conduction problems," Applied Mathematics and Computation, Elsevier, vol. 449(C).
    • Handle: RePEc:eee:apmaco:v:449:y:2023:i:c:s0096300323000863
    DOI: 10.1016/j.amc.2023.127917
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