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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Unique continuation along curves and hypersurfaces for second order anisotropic hyperbolic systems with real analytic coefficients


Authors: Jin Cheng, Ching-Lung Lin and Gen Nakamura
Journal: Proc. Amer. Math. Soc. 133 (2005), 2359-2367
MSC (2000): Primary 35B60, 35L05
Published electronically: March 17, 2005
MathSciNet review: 2138878
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Abstract: In this paper we prove the following kind of unique continuation property. That is, the zero on each geodesic of the solution in a real analytic hypersurface for second order anisotropic hyperbolic systems with real analytic coefficients can be continued along this curve.


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Additional Information

Jin Cheng
Affiliation: Department of Mathematics, Fudan University, Shanghai 200433, People’s Republic of China
Email: jcheng@fudan.edu.cn

Ching-Lung Lin
Affiliation: Department of Mathematics, National Chung-Cheng University, Chia-Yi 62117, Taiwan
Email: cllin@math.ccu.edu.tw

Gen Nakamura
Affiliation: Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan
Email: gnaka@math.sci.hokudai.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07782-8
PII: S 0002-9939(05)07782-8
Keywords: Unique continuation, anisotropic hyperbolic system, analytic coefficients, localized Fourier-Gauss transform
Received by editor(s): December 12, 2003
Published electronically: March 17, 2005
Additional Notes: The first author was supported in part by NSF of China (No. 10431030), Shuguang Project of Shanghai Municipal Education Commission and the China State Major Basic Research Project 2001CB309400. The second author was supported in part by the Taiwan National Science Foundation. The third author was supported in part by Grant-in-Aid for Scientific Research (B)(2) (No.14340038) of the Japan Society for the Promotion of Science.
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2005 American Mathematical Society