Nonlinear wave equations and singular solutions
Author:
Hideshi Yamane
Journal:
Proc. Amer. Math. Soc. 135 (2007), 3659-3667
MSC (2000):
Primary 35L70, 35A20
DOI:
https://doi.org/10.1090/S0002-9939-07-08926-5
Published electronically:
August 14, 2007
MathSciNet review:
2336582
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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:
https://doi.org/10.1090/S0002-9939-07-08926-5
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.
