Logarithmic stability of parabolic Cauchy problems

2017/02/21 by Mourad Choulli, Masahiro Yamamoto, Choulli, Mourad +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1702.06299

openalex publication_date 2017/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The uniqueness of parabolic Cauchy problems is nowadays a classical problem and since Hadamard \citeHa 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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