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Identifiability and stability results of one emerging crack in heterogeneous media by one boundary measurements
Author(s) -
Nicaise Serge,
Zaïr Ouahiba
Publication year - 2001
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/mma.246
Subject(s) - lipschitz continuity , identifiability , mathematics , stability (learning theory) , boundary (topology) , plane (geometry) , mathematical analysis , inverse problem , boundary value problem , inverse , geometry , computer science , statistics , machine learning
We consider the inverse problem of determining one emerging crack in a plane heterogeneous medium. We show that one measurement on a part of the boundary with appropriate flux uniquely determines such a crack. We further establish a local Lipschitz continuity result. At the end, we give an approximation result for the nonstationary heat equation. Copyright © 2001 John Wiley & Sons, Ltd.