Logarithmic stability of parabolic Cauchy problems

Mourad Choulli (1) , Masahiro Yamamoto (2)

1 EDP - Equations aux dérivées partielles
2 Graduate School of Mathematical Sciences

The uniqueness of parabolic Cauchy problems is nowadays a classical problem and since Hadamard [4] 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 in the stability for parabolic Cauchy problems. In the present article, we bring the complete answer to this issue.

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

Domaines: Equations aux dérivées partielles [math.AP]

Mourad Choulli, Masahiro Yamamoto. Logarithmic stability of parabolic Cauchy problems. 2017. ⟨hal-01472597v1⟩