Geodesic
The factorization method for cracks in inhomogeneous media
Applications of Mathematics, Tome 62 (2017) no. 5, pp. 509-533 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We consider the inverse scattering problem of determining the shape and location of a crack surrounded by a known inhomogeneous media. Both the Dirichlet boundary condition and a mixed type boundary conditions are considered. In order to avoid using the background Green function in the inversion process, a reciprocity relationship between the Green function and the solution of an auxiliary scattering problem is proved. Then we focus on extending the factorization method to our inverse shape reconstruction problems by using far field measurements at fixed wave number. We remark that this is done in a non intuitive space for the mixed type boundary condition as we indicate in the sequel.
We consider the inverse scattering problem of determining the shape and location of a crack surrounded by a known inhomogeneous media. Both the Dirichlet boundary condition and a mixed type boundary conditions are considered. In order to avoid using the background Green function in the inversion process, a reciprocity relationship between the Green function and the solution of an auxiliary scattering problem is proved. Then we focus on extending the factorization method to our inverse shape reconstruction problems by using far field measurements at fixed wave number. We remark that this is done in a non intuitive space for the mixed type boundary condition as we indicate in the sequel.
DOI : 10.21136/AM.2017.0194-16
Classification : 45Q05
Keywords: inverse scattering; factorization method; crack; inhomogeneous media 
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     title = {The factorization method for cracks in inhomogeneous media},
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     year = {2017},
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Guo, Jun; Yan, Guozheng; Jin, Jing; Hu, Junhao. The factorization method for cracks in inhomogeneous media. Applications of Mathematics, Tome 62 (2017) no. 5, pp. 509-533. doi: 10.21136/AM.2017.0194-16

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