Year: 2022
Author: Thouraya Baranger Nouri, Faker Ben Belgacem
Journal of Mathematical Study, Vol. 55 (2022), Iss. 1 : pp. 38–53
Abstract
We study the ill-posedness degree of the reconstruction processes of missing boundary data or initial states in the transient heat conduction. Both problems are severely ill-posed. This is a powerful indicator about the way the instabilities will affect the computations in the numerical recovery methods. We provide rigorous proofs of this result where the conductivites are space dependent. The theoretical work is concerned with the unsteady heat equation in one dimension even though most of the results obtained here are readily extended to higher dimensions.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v55n1.22.03
Journal of Mathematical Study, Vol. 55 (2022), Iss. 1 : pp. 38–53
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Data completion process ill-posedness degree Cauchy matrix convolution equations parabolic regularity.