Modified transmission eigenvalues in inverse scattering theory
| Autor: | Shixu Meng, Peter Monk, Samuel Cogar, David Colton |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Field (physics)
Scattering Applied Mathematics Operator (physics) Mathematical analysis Plane wave 010103 numerical & computational mathematics 01 natural sciences Computer Science Applications Theoretical Computer Science 010101 applied mathematics Signal Processing Inverse scattering problem Scattering theory Quantum inverse scattering method 0101 mathematics Mathematical Physics Eigenvalues and eigenvectors Mathematics |
| Zdroj: | Inverse Problems. 33:125002 |
| ISSN: | 1361-6420 0266-5611 |
| Popis: | We consider the scattering of an acoustic plane wave by an inhomogeneous medium of compact support. Our aim is to introduce a new class of target signatures that can be used to detect changes in the material properties of the scattering object from a knowledge of the far field pattern of the scattered field. To this end we introduce a modified far field operator depending on a parameter η and show that this operator is injective with dense range provided η is not an eigenvalue of a new problem called the modified transmission eigenvalue problem. It is explained why this class of target signatures is preferable in some ways to previously studied target signatures that are based on scattering resonances, transmission eigenvalues, or Stekloff eigenvalues. |
| Databáze: | OpenAIRE |
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