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 - <p style="text-align: justify;">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.</p>