Event Date
2012-04-23
Event Time
02:03 pm ~ 03:20 pm
Event Location
Wachman 617
Abstract: The transmission eigenvalue problem is a new class of eigenvalue
problems that has recently appeared in inverse scattering theory for inhomogeneous media. Such eigenvalues provide information about material properties of
the scattering object and can be determined from scattering data, hence can play
an important role in a variety of problems in target identification. The transmission
eigenvalue problem is non-selfadjoint and nonlinear which make its mathematical
investigation very interesting.
In this lecture we will describe how the transmission eigenvalue problem arises
in scattering theory, how transmission eigenvalues can be computed from scattering
data and what is known mathematically about these eigenvalues. The investigation of transmission eigenvalue problem for anisotropic media will be discussed
and Faber-Krahn type inequalities for the first real transmission eigenvalue will be
presented.
We conclude our presentation with some recent preliminary results on transmission eigenvalues for absorbing and dispersive media, i.e. with complex valued index
of refraction, as well as for anisotropic media with contrast that changes sign.
Our presentation contains a collection of results obtained with several collaborators, in particular with David Colton, Drossos Gintides, Houssem Haddar and
Andreas Kirsch.