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Geometric control in the presence of a black box


Authors: Nicolas Burq and Maciej Zworski
Journal: J. Amer. Math. Soc. 17 (2004), 443-471
MSC (2000): Primary 35B37, 35P20, 81Q20
DOI: https://doi.org/10.1090/S0894-0347-04-00452-7
Published electronically: February 3, 2004
MathSciNet review: 2051618
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Abstract: We apply the “black box scattering” point of view to problems in control theory for the Schrödinger equation and in high energy eigenvalue scarring. We show how resolvent bounds with origins in scattering theory, combined with semi-classical propagation, give quantitative control estimates. We also show how they imply control for time dependent problems.


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Additional Information

Nicolas Burq
Affiliation: Université Paris Sud, Mathématiques, Bât 425, 91405 Orsay Cedex, France
MR Author ID: 315457
Email: Nicolas.burq@math.u-psud.fr

Maciej Zworski
Affiliation: Mathematics Department, University of California, Evans Hall, Berkeley, California 94720
MR Author ID: 227055
Email: zworski@math.berkeley.edu

Received by editor(s): May 14, 2003
Published electronically: February 3, 2004
Article copyright: © Copyright 2004 American Mathematical Society