Determination of a Linear Crack in an Elastic Body from Boundary Measurements—Lipschitz Stability

2008 ◽  
Vol 40 (3) ◽  
pp. 984-1002 ◽  
Author(s):  
Elena Beretta ◽  
Elisa Francini ◽  
Sergio Vessella
2014 ◽  
Vol 46 (4) ◽  
pp. 2692-2729 ◽  
Author(s):  
Giovanni Alessandrini ◽  
Michele Di Cristo ◽  
Antonino Morassi ◽  
Edi Rosset

Author(s):  
Lucie Baudouin ◽  
Eduardo Cerpa ◽  
Emmanuelle Crépeau ◽  
Alberto Mercado

AbstractThis paper concerns the inverse problem of retrieving the principal coefficient in a Korteweg–de Vries (KdV) equation from boundary measurements of a single solution. The Lipschitz stability of this inverse problem is obtained using a new global Carleman estimate for the linearized KdV equation. The proof is based on the Bukhgeĭm–Klibanov method.


2010 ◽  
Vol 26 (8) ◽  
pp. 085015 ◽  
Author(s):  
Elena Beretta ◽  
Elisa Francini ◽  
Eunjoo Kim ◽  
June-Yub Lee

2001 ◽  
Vol 17 (4) ◽  
pp. 1127-1139 ◽  
Author(s):  
A El Badia ◽  
T Ha-Duong

1996 ◽  
Vol 27 (2) ◽  
pp. 361-375 ◽  
Author(s):  
Giovanni Alessandrini ◽  
Elena Beretta ◽  
Sergio Vessella

2015 ◽  
Vol 2015 ◽  
pp. 1-22 ◽  
Author(s):  
Ali Golsoorat Pahlaviani ◽  
Suren Mkhitaryan

The stress state of a bimaterial elastic body that has a row of cracks on an interface surface is considered. It is subjected to antiplane deformations by uniformly distributed shear forces acting on the horizontal sides of the body. The governing equations of the problem, the stress intensity factors, the deformation of the crack edges, and the shear stresses are derived. The solution of the problem via the Fourier sine series is reduced to the determination of a singular integral equation (SIE) and consequently to a system of linear equations. In the end, the problem is solved in special cases with inclusions. The results of this paper and the previously published results show that the used approach based on the Gauss-Chebyshev quadrature method can be considered as a generalized procedure to solve the collinear crack problems in mode I, II, or III loadings.


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