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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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An inverse problem for the wave equation

1Department of Mathematics, University of West Georgia, Carrollton, GA 30118, USA.

Citation Information: Journal of Inverse and Ill-posed Problems. Volume 19, Issue 4-5, Pages 573–592, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: 10.1515/jiip.2011.056, November 2011

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In the first part of this article, we show that we can recover the coefficient q in the one-dimensional wave equation from a finite number of special lateral measurements. Moreover, if some estimates on the size of q are available, then q can be recovered from a single boundary measurement. In the second part we treat the multidimensional case and show how we can reconstruct the coefficient q from a sequence of boundary measurements taken at one point only.

Keywords.: Inverse wave equation; inverse spectral theory; spectral estimation; initial-to-boundary map

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