In the context of a steady state, sourceless inverse heat conduction problem in an open bounded domain Ω containing a crack σ, the point-source reciprocity gap function gσ[⋅] is defined. The identification of σ is transformed into parameter fitting. In the Conclusions it is conjectured that "several cracklets may lead to the detection of several cracks'', not just approximate location and direction. This reviewer believes that the cracklet notion may induce interesting developments in multiscale geometric analysis [e.g., E. J. Candès, Notices Amer. Math. Soc. 50 (2003), no. 11, 1402--1403; MR2011606].
Crosta, G. (2005). Mathematical Review: MR2078817 (2005h:74024) Alves, Carlos J. S.; Abdallah, Jalel Ben; Jaoua, Mohamed Recovery of cracks using a point-source reciprocity gap function. MATHEMATICAL REVIEWS.
Mathematical Review: MR2078817 (2005h:74024) Alves, Carlos J. S.; Abdallah, Jalel Ben; Jaoua, Mohamed Recovery of cracks using a point-source reciprocity gap function
CROSTA, GIOVANNI FRANCO FILIPPO
2005
Abstract
In the context of a steady state, sourceless inverse heat conduction problem in an open bounded domain Ω containing a crack σ, the point-source reciprocity gap function gσ[⋅] is defined. The identification of σ is transformed into parameter fitting. In the Conclusions it is conjectured that "several cracklets may lead to the detection of several cracks'', not just approximate location and direction. This reviewer believes that the cracklet notion may induce interesting developments in multiscale geometric analysis [e.g., E. J. Candès, Notices Amer. Math. Soc. 50 (2003), no. 11, 1402--1403; MR2011606].
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