|
Unique continuation along curves and hypersurfaces for second order anisotropic hyperbolic systems with real analytic coefficients
Author(s):
Jin
Cheng;
Ching-Lung
Lin;
Gen
Nakamura
Journal:
Proc. Amer. Math. Soc.
133
(2005),
2359-2367.
MSC (2000):
Primary 35B60, 35L05
Posted:
March 17, 2005
Retrieve article in:
PDF DVI PostScript
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.
References:
-
- 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)
Similar Articles:
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:
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
Posted:
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
Copyright of article:
Copyright
2005,
American Mathematical Society
|
Comments: webmaster@ams.org