Logarithmic stability of parabolic Cauchy problems

Mourad Choulli (1) , Masahiro Yamamoto (2)

1 IECL - Institut Élie Cartan de Lorraine
2 Graduate School of Mathematical Sciences

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.

Mots clés: logarithmic stability; Parabolic Cauchy problems; Carleman inequality; Hardy inequality

Domaines: Equations aux dérivées partielles [math.AP]

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