6·î5Æü(ÌÚ) 16:00 -- 17:00 Prof. David Colton (University of Delaware, USA)
``The Inverse Scattering Problem for an Isotropic Medium''
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This talk is concerned with the inverse electromagnetic scattering problem
for an isotropic inhomogeneous infinite cylinder. After formulating the
direct scattering problem we proceed to the inverse scattering problem which
is the main theme of this lecture. After discussing what is known about
uniqueness for the inverse problem, we will proceed to the definition and
properties of the far field operator. This leads to the study of a rather
unusual spectral problem for partial differential equations called the
interior transmission problem. We will state what is known about this
problem including its role in determining lower bounds for the index of
refraction from a knowledge of the far field pattern of the scattered wave.
The talk is concluded by briefly considering the case of limited aperture
data,in particular the use of the gap reciprocity method to determine the
shape and location of buried objects. Numerical examples will be given as
well as a number of open problems.