Inverse Backscattering Problem for the Acoustic Equation in Even Dimensions
Journal
Journal of Mathematical Analysis and Applications
Journal Volume
220
Journal Issue
2
Pages
676-696
Date Issued
1998
Author(s)
Wang, J.-N.
Abstract
We show that the sound speedc(x) of the acoustic wave equation in any even dimension can be uniquely determined by the backscattering data provided that it is close to a constant. In the three-dimensional case, P. Stefanov and G. Uhlmann (SIAM J. Math. Anal.28,1997, 1191-1204) have proved a similar result. Their method takes advantage of the inversion formula for the Radon transform in odd dimensions being a local operator. This is not true in even dimensions. Moreover, the odd-dimensional Lax and Phillips modified Radon transform fails to work in even dimensions. In this paper, we overcome these difficulties and prove an even-dimensional version of Stefanov and Uhlmann's result. © 1998 Academic Press.
Type
journal article