zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
The inverse electromagnetic scattering problem in a piecewise homogeneous medium. (English) Zbl 1219.35363
The paper is concerned with the problem of scattering of time-harmonic electromagnetic waves from an impenetrable obstacle in a piecewise homogeneous medium, which widely occur in practical applications. The case where the obstacle is buried in a two-layered piecewise homogeneous medium is considered but the results can be extended to the multi-layered case. The well-posedness of the corresponding direct problem is established by means of the integral equation method. It was proved previously [see {\it X. Liu} and {\it B. Zang}, Appl. Anal. 88, No. 9, 1339--1355 (2009; Zbl 1176.78010)], under the condition that the wave numbers in the innermost and outmost homogeneous layers coincide and $S_0$ is known in advance, that the obstacle with its physical property can be uniquely determined from knowledge of the electric far-field pattern for incident plane waves. In the present paper this restriction is removed by establishing a new mixed reciprocity relation. It is proved that the penetrable interface between layers can also be uniquely determined.

35R30Inverse problems for PDE
78A46Inverse scattering problems
Full Text: DOI arXiv