Identifiability and stability results of one emerging crack in heterogeneous media by one boundary measurements

Authors
Nicaise, S Zair, O
Citation
S. Nicaise et O. Zair, Identifiability and stability results of one emerging crack in heterogeneous media by one boundary measurements, MATH METH A, 24(12), 2001, pp. 865-884
Citations number
22
Categorie Soggetti
Mathematics
Journal title
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
ISSN journal
01704214 → ACNP
Volume
24
Issue
12
Year of publication
2001
Pages
865 - 884
Database
ISI
SICI code
0170-4214(200108)24:12<865:IASROO>2.0.ZU;2-Z
Abstract
We consider the inverse problem of determining one emerging crack in a plan e heterogeneous medium. We show that one measurement on a part of the bound ary with appropriate flux uniquely determines such a crack. We further esta blish a local Lipschitz continuity result. At the end, we give an approxima tion result for the nonstationary heat equation. Copyright (C) 2001 John Wi ley & Sons, Ltd.