A variational technique of mollification applied to backward heat conduction problems
From MaRDI portal
Publication:6391741
DOI10.1016/J.AMC.2023.127917zbMath1511.35009arXiv2202.10264MaRDI QIDQ6391741
Publication date: 21 February 2022
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.
This page was built for publication: A variational technique of mollification applied to backward heat conduction problems
