The Factorization Method for an inverse fluid-solid interaction scattering problem | Zendy

Andreas Kirsch | Zendy; Albert L. Ruiz | Zendy

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The Factorization Method for an inverse fluid-solid interaction scattering problem

Author(s) -

Andreas Kirsch,

Albert L. Ruiz

Publication year - 2012

Publication title -

inverse problems and imaging

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.755

H-Index - 40

eISSN - 1930-8345

pISSN - 1930-8337

DOI - 10.3934/ipi.2012.6.681

Subject(s) - factorization , eigenvalues and eigenvectors , inverse scattering problem , scattering , operator (biology) , set (abstract data type) , plane (geometry) , inverse problem , plane wave , function (biology) , field (mathematics) , matrix decomposition , mathematics , computer science , mathematical analysis , mathematical optimization , physics , algorithm , pure mathematics , geometry , optics , repressor , chemistry , biochemistry , quantum mechanics , transcription factor , programming language , gene , biology , evolutionary biology

In this paper we justify the Factorization Method for a coupled acoustic-elastic medium. Under natural assumptions on the data we prove an explicit form of the characteristic function of the scattering medium $D$ where only the spectral data of the far field operator enter. This information is provided by the knowledge of the far field patterns for all incident plane waves. In the last section we investigate the corresponding interior transmission eigenvalue problem and prove that the eigenvalues form a discrete set.

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