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On the inverse emergent plane crack problem
Author(s) -
Andrieux Stéphane,
Abda Amel Ben,
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(19980710)21:10<895::aid-mma975>3.0.co;2-1
Subject(s) - mathematics , identifiability , uniqueness , plane (geometry) , stability (learning theory) , inverse problem , domain (mathematical analysis) , mathematical analysis , boundary (topology) , inverse , derivative (finance) , boundary value problem , geometry , computer science , statistics , machine learning , financial economics , economics
This paper deals with the detection of emergent plane cracks, by using boundary measurements. An identifiability result (uniqueness of the solution) is first proved. Then, we look at the stability of this solution with respect to the measurement. A weak stability result is proved, as well as a Lipshitz stability result for straight cracks, by using domain‐derivative techniques. © 1998 B. G. Teubner Stuttgart—John Wiley & Sons, Ltd.