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Preprints, Working Papers, ... Year : 2018

Logarithmic stability of parabolic Cauchy problems

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.
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Dates and versions

hal-01472597 , version 1 (21-02-2017)
hal-01472597 , version 2 (04-06-2017)
hal-01472597 , version 3 (03-06-2018)

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Cite

Mourad Choulli, Masahiro Yamamoto. Logarithmic stability of parabolic Cauchy problems. 2018. ⟨hal-01472597v3⟩
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