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)
On the uniqueness of a spherically symmetric speed of sound from transmission eigenvalues. (English) Zbl 0803.35163
Summary: Consider the inverse acoustic scattering problem for spherically symmetric inhomogeneity of compact support. Define the corresponding homogeneous and inhomogeneous interior transmission problems. We study the subset of transmission eigenvalues corresponding to spherically symmetric eigenfunctions of the homogeneous interior transmission problem. These transmission eigenvalues are shown to be zeros of the scattering amplitude and also the set of eigenvalues of a special Sturm- Liouville problem. A uniqueness theorem for the potential of the derived Sturm-Liouville problem is proved when the data are the given spectra and partial knowledge of the potential. A corollary of this theorem is a uniqueness theorem for the original inverse acoustic scattering problem.

35R30Inverse problems for PDE
76Q05Hydro- and aero-acoustics
35P25Scattering theory (PDE)
Full Text: DOI