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On a non‐linear geometrical inverse problem of Signorini type: identifiability and stability
Author(s) -
Abda Amel Ben,
Chaabane Slim,
Dabaghi Fadi El,
Jaoua Mohamed
Publication year - 1998
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(199810)21:15<1379::aid-mma999>3.0.co;2-f
Subject(s) - identifiability , mathematics , lipschitz continuity , inverse problem , stability (learning theory) , boundary (topology) , type (biology) , inverse , mathematical analysis , geometry , statistics , ecology , machine learning , computer science , biology
This paper deals with a non‐linear inverse problem of identification of unknown boundaries, on which the prescribed conditions are of Signorini type. We first prove an identifiability result, in both frameworks of thermal and elastic testing. Local Lipschitz stability of the solutions with respect to the boundary measurements is also established, in case of unknown boundaries which are parts of 1, β Jordan curves, with β>0. © 1998 B. G. Teubner Stuttgart—John Wiley & Sons, Ltd.