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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Transmission Eigenvalues in Inverse Scattering The
ory - Cakoni\, F (University of Delaware)
DTSTART;TZID=Europe/London:20110803T161500
DTEND;TZID=Europe/London:20110803T170000
UID:TALK32220AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/32220
DESCRIPTION:The transmission eigenvalue problem is a new class
of eigenvalue problems that has recently appeared
in inverse scattering theory for inhomogeneous me
dia. Such eigenvalues provide information about ma
terial properties of the scattering object and can
be determined from scattering data\, hence can pl
ay an important role in a variety of problems in t
arget identification. The transmission eigenvalue
problem is non-selfadjoint and nonlinear which mak
e its mathematical investigation very interesting.
\n\nIn this lecture we will describe how the tran
smission eigenvalue problem arises in scattering t
heory\, how transmission eigenvalues can be comput
ed from scattering data and what is known mathemat
ically about these eigenvalues. The investigation
of transmission eigenvalue problem for anisotropic
media will be discussed and Faber-Krahn type ineq
ualities for the first real transmission eigenvalu
e will be presented. We conclude our presentation
with some recent preliminary results on transmissi
on eigenvalues for absorbing and dispersive media\
, i.e. with complex valued index of refraction\, a
s well as for anisotropic media with contrast that
changes sign. \n\nOur presentation contains a col
lection of results obtained with several collabora
tors\, in particular with David Colton\, Drossos G
intides\, Houssem Haddar and Andreas Kirsch. \n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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