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

 

Nonlinear wave equations and singular solutions


Author: Hideshi Yamane
Journal: Proc. Amer. Math. Soc. 135 (2007), 3659-3667
MSC (2000): Primary 35L70, 35A20
Published electronically: August 14, 2007
MathSciNet review: 2336582
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Abstract: We construct solutions to nonlinear wave equations that are singular along a prescribed noncharacteristic hypersurface, which is the graph of a function satisfying not the Eikonal but another partial differential equation of the first order. The method of Fuchsian reduction is employed.


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Additional Information

Hideshi Yamane
Affiliation: Department of Physics, Kwansei Gakuin University, Gakuen 2-1, Sanda, Hyougo 669-1337, Japan
Email: yamane@ksc.kwansei.ac.jp; yamanehideshi@95.alumni.u-tokyo.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08926-5
PII: S 0002-9939(07)08926-5
Keywords: Nonlinear wave equation, nonlinear Fuchsian equation, singular Cauchy problem
Received by editor(s): March 21, 2006
Received by editor(s) in revised form: September 8, 2006
Published electronically: August 14, 2007
Additional Notes: This research was partially supported by Grant-in-Aid for Scientific Research (No.17540182), Japan Society for the Promotion of Science.
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.