Recovery of a source term or a speed with one measurement and applications
Authors:
Plamen Stefanov and Gunther Uhlmann
Journal:
Trans. Amer. Math. Soc. 365 (2013), 5737-5758
MSC (2010):
Primary 35L05, 35R30
DOI:
https://doi.org/10.1090/S0002-9947-2013-05703-0
Published electronically:
April 25, 2013
MathSciNet review:
3091263
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: We study the problem of recovery of the source in the wave equation in anisotropic medium with
known so that
, with a single measurement. We use Carleman estimates combined with geometric arguments and give sharp conditions for uniqueness. We also study the non-linear problem of recovery of the sound speed in the equation
with one measurement. We give sharp conditions for stability as well. An application to thermoacoustic tomography is also presented.
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Additional Information
Plamen Stefanov
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Gunther Uhlmann
Affiliation:
Department of Mathematics, University of Washington, Seattle, Washington 98195
DOI:
https://doi.org/10.1090/S0002-9947-2013-05703-0
Received by editor(s):
March 13, 2011
Received by editor(s) in revised form:
August 10, 2011
Published electronically:
April 25, 2013
Additional Notes:
The first author was partially supported by an NSF Grant DMS-0800428 and a Simons Visiting Professorship
The second author was partially supported by an NSF, a Senior Clay Award and Chancellor Professorship at the University of California, Berkeley
Article copyright:
© Copyright 2013
American Mathematical Society