We treat the stability issue for an inverse problem arising from nondestructive evaluation by thermal imaging. We consider the determination of an unknown portion of the boundary of a thermic conducting body by overdetermined boundary data for a parabolic initial-boundary value problem.We obtain that when the unknown part of the boundary is a priori known to be smooth, the data are as regular as possible and all possible measurements are taken into account, the problem is exponentially ill-posed. Then, we prove that a single measurement with some a priori information on the unknown part of the boundary and minimal assumptions on the data, in particular on the thermal conductivity, is enough to have stable determination of the unknown boundary. Given the exponential illposedness, the stability estimate obtained is optimal.

Stability properties of an inverse parabolic problem with unknown boundaries / DI CRISTO M.; RONDI L.; S. VESSELLA. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - STAMPA. - 185:(2006), pp. 223-255. [10.1007/s10231-005-0152-x]

Stability properties of an inverse parabolic problem with unknown boundaries

VESSELLA, SERGIO
2006

Abstract

We treat the stability issue for an inverse problem arising from nondestructive evaluation by thermal imaging. We consider the determination of an unknown portion of the boundary of a thermic conducting body by overdetermined boundary data for a parabolic initial-boundary value problem.We obtain that when the unknown part of the boundary is a priori known to be smooth, the data are as regular as possible and all possible measurements are taken into account, the problem is exponentially ill-posed. Then, we prove that a single measurement with some a priori information on the unknown part of the boundary and minimal assumptions on the data, in particular on the thermal conductivity, is enough to have stable determination of the unknown boundary. Given the exponential illposedness, the stability estimate obtained is optimal.
2006
185
223
255
DI CRISTO M.; RONDI L.; S. VESSELLA
File in questo prodotto:
File Dimensione Formato  
DC_Ron_Vess.pdf

Accesso chiuso

Tipologia: Versione finale referata (Postprint, Accepted manuscript)
Licenza: Tutti i diritti riservati
Dimensione 527.1 kB
Formato Adobe PDF
527.1 kB Adobe PDF   Richiedi una copia

I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/225919
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 23
  • ???jsp.display-item.citation.isi??? 22
social impact