Logarithmic stability of parabolic Cauchy problems
Analysis of PDEs
2020-11-06 v4
Abstract
The uniqueness of parabolic Cauchy problems is nowadays a classical problem and since Hadamard \cite{Ha} these kind of problems are known to be ill-posed and even severely ill-posed. Until now there are only few partial results concerning the quantification of the stability for parabolic Cauchy problems. In the present article, we bring the complete answer to this issue, provided that the space domain has finite diameter with respect to the geodesic distance and assuming that solutions are sufficiently smooth.
Cite
@article{arxiv.1702.06299,
title = {Logarithmic stability of parabolic Cauchy problems},
author = {Mourad Choulli and Masahiro Yamamoto},
journal= {arXiv preprint arXiv:1702.06299},
year = {2020}
}