The fixed angle scattering problem for the wave equation
Speaker |
Prof. Rakesh,
University of Delaware, USA
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When |
Jul 31, 2019
from 04:00 PM to 05:00 PM |
Where | LH 006 |
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Abstract: A three dimensional acoustic medium (operator is ☐+ q(x)) is probed by a plane wave coming from one specific direction and the “far field pattern” of the scattered wave is measured in all directions and for all time delays. A long standing open problem is the recovery of the acoustic property of the medium (the coefficient q(x)) from this far-field data. This corresponds to proving the injectivity of and inverting a nonlinear map defined for all compactly supported smooth functions in three dimensions. We will talk about our (with Mikko Salo of the University of Jyvaskyla) injectivity result over the subdomain of functions which are even in the direction of the incoming wave.