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
DOI:
https://doi.org/10.1090/S0002-9939-05-07782-8
Published electronically:
March 17, 2005
MathSciNet review:
2138878
Full-text PDF
Abstract | References | Similar Articles | Additional Information
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.
- 1. J. Cheng, Y.C. Hon & M. Yamamoto, Stability in line unique continuation of harmonic functions: general dimensions, Inverse and Ill-Posed Problems 6(1998), 319-326. MR 1652109 (2000b:35034)
- 2. J. Cheng & M. Yamamoto, Unique continuation on a line for harmonic functions, Inverse Problems 14 (1998), 869-882. MR 1642532 (99d:35029)
- 3. J. Cheng, M. Yamamoto & Q. Zhou, Unique continuation on a hyperplane for wave equation, Chin. Ann. of Math. 20B 4 (1999), 385-392. MR 1752740 (2001f:35232)
- 4. L. Hörmander, The analysis of linear partial differential operators, Vol. 1, 2nd Edition, Springer-Verlag, Berlin/New York, 1990. MR 1996773
- 5. H. Kumano-go, Pseudodifferential operators, Massachusetts Institute of Technology, 1981. MR 0666870 (84c:35113)
- 6. N. Lerner, Uniqueness for an ill-posed problem, J. Diff. Eq., 71 (1988), 255-260. MR 0927001 (89a:35126)
- 7. S. Mizohata, The theory of partial differential equations, Cambridge University Press, 1973. MR 0599580 (58:29033)
- 8. M. Ohtsu, S. Yuyama & T. Imanaka, Theoretical treatment of acoustic emission sources in microfracturing due to disbonding, J. Acoustical Soc. America 82(1987), 506-512.
- 9. L. Robbiano, Théorème d'unicité adapté au contrôle des solutions des problèmes hyperboliques, Communication in P.D.E. 16 (1991), 789-800. MR 1113107 (92j:35002)
Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 35B60, 35L05
Retrieve articles in all journals with MSC (2000): 35B60, 35L05
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:
https://doi.org/10.1090/S0002-9939-05-07782-8
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