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Perspectives on

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Paola Elefante

on 25 August 2015

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Transcript of Perspectives on

Perspectives on
Transmission Eigenvalues

Inverse Problems in Finland
Δw +
k
²
n(x)
w = 0 in D
Δv +
k
² v = 0 in D
v-w = ∂v-∂w = 0 on ∂D
What is an inverse problem?
Mathematics
regularity of boundary and TEs
size of cavity and first TE
less assumptions (ex. absorption case)
Physics
physical meaning of TEs
relationship between TEs and physical properties
...
Image deblurring
X-ray Computed Tomography
Travel Time Tomography
cause
effect
Paola Elefante
University of Helsinki

Inverse Acoustic Scattering
The Interior Transmission Problem
Transmission eigenvalues
infinitely many
discrete (non-dense) set
exist under quite weak assumptions
can be non-scattering frequencies
Open questions
Thank you for your attention.
Suggested source:
Cakoni - Haddar, "
Transmission Eigenvalues
", Inv. Pr. 29 (2013), editorial.
Engineering
possible applications
when acoustic waves are better than x-rays?
...
Why Trasmission eigenvalues are important
They carry information about
n(x)
.
Full transcript