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.