TY - JOUR
T1 - Cauchy Matrices in the Observation of Diffusion Equations
AU - Ben Belgacem , Faker
AU - Kaber , Sidi-Mahmoud
JO - Journal of Mathematical Study
VL - 4
SP - 330
EP - 344
PY - 2015
DA - 2015/12
SN - 48
DO - http://doi.org/10.4208/jms.v48n4.15.02
UR - https://global-sci.org/intro/article_detail/jms/9937.html
KW - Pick matrices, Cauchy matrices, Hadamard product, diffusion equation, observability inequalities.
AB - <p style="text-align: justify;">Observability Gramians of diffusion equations have been recently connected
to infinite Pick and Cauchy matrices. In fact, inverse or observability inequalities can
be obtained after estimating the extreme eigenvalues of these structured matrices,with
respect to the diffusion semi-group matrix. The purpose is hence to conduct a spectral
study of a subclass of symmetric Cauchy matrices and present an algebraic way to
show the desired observability results. We revisit observability inequalities for three
different observation problems of the diffusion equation and show how they can be
(re)stated through simple proofs.</p>