Volume 55, Issue 1
Data Recovery from Cauchy Measurements in Transient Heat Transfer

Thouraya Baranger Nouri & Faker Ben Belgacem

J. Math. Study, 55 (2022), pp. 38-53.

Published online: 2022-01

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  • 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.

  • Keywords

Data completion process, ill-posedness degree, Cauchy matrix, convolution equations, parabolic regularity.

  • AMS Subject Headings

52B10, 65D18, 68U05, 68U07

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

thouraya.baranger@univ-lyon1.fr (Thouraya Baranger Nouri)

faker.ben-belgacem@utc.fr (Faker Ben Belgacem)

  • BibTex
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  • TXT
@Article{JMS-55-38, author = {Thouraya and Baranger Nouri and thouraya.baranger@univ-lyon1.fr and 22005 and Université de Lyon, Université Lyon 1, LMC2, EA 7427, F69622 Villeurbanne Cedex, France and Thouraya Baranger Nouri and Faker and Ben Belgacem and faker.ben-belgacem@utc.fr and 13293 and Alliance Sorbonne Université, UTC, EA 2222, Laboratoire de Mathématiques Appliquées de Compiègne, F-60205 Compiègne, France and Faker Ben Belgacem}, title = {Data Recovery from Cauchy Measurements in Transient Heat Transfer}, journal = {Journal of Mathematical Study}, year = {2022}, volume = {55}, number = {1}, pages = {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.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v55n1.22.03}, url = {http://global-sci.org/intro/article_detail/jms/20192.html} }
TY - JOUR T1 - Data Recovery from Cauchy Measurements in Transient Heat Transfer AU - Baranger Nouri , Thouraya AU - Ben Belgacem , Faker JO - Journal of Mathematical Study VL - 1 SP - 38 EP - 53 PY - 2022 DA - 2022/01 SN - 55 DO - http://doi.org/10.4208/jms.v55n1.22.03 UR - https://global-sci.org/intro/article_detail/jms/20192.html KW - Data completion process, ill-posedness degree, Cauchy matrix, convolution equations, parabolic regularity. AB -

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.

Thouraya Baranger Nouri & Faker Ben Belgacem. (2022). Data Recovery from Cauchy Measurements in Transient Heat Transfer. Journal of Mathematical Study. 55 (1). 38-53. doi:10.4208/jms.v55n1.22.03
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