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Uniqueness in inverse acoustic and electromagnetic scattering by penetrable obstacles with embedded objects.
- Source :
-
Journal of Differential Equations . Dec2018, Vol. 265 Issue 12, p6352-6383. 32p. - Publication Year :
- 2018
-
Abstract
- Abstract This paper considers the inverse problem of scattering of time-harmonic acoustic and electromagnetic plane waves by a bounded, inhomogeneous, penetrable obstacle with embedded objects inside. A new method is proposed to prove that the inhomogeneous penetrable obstacle can be uniquely determined from the far-field pattern at a fixed frequency, disregarding its contents. Our method is based on constructing a well-posed interior transmission problem in a small domain associated with the Helmholtz or modified Helmholtz equation and the Maxwell or modified Maxwell equations. A key role is played by the smallness of the domain which ensures that the lowest transmission eigenvalue is large so that a given wave number k is not an eigenvalue of the interior transmission problem. Another ingredient in our proofs is a priori estimates of solutions to the transmission scattering problems with data in L p (1 < p < 2), which are established in this paper by using the integral equation method. A main feature of the new method is that it can deal with the acoustic and electromagnetic cases in a unified way and can be easily applied to deal with inverse scattering by unbounded rough interfaces. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00220396
- Volume :
- 265
- Issue :
- 12
- Database :
- Academic Search Index
- Journal :
- Journal of Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 132486673
- Full Text :
- https://doi.org/10.1016/j.jde.2018.07.033