Proceedings of the American Mathematical Society

Author(s): Hideshi Yamane
Journal: Proc. Amer. Math. Soc. 135 (2007), 3659-3667.
MSC (2000): Primary 35L70, 35A20
Posted: August 14, 2007
Retrieve article in: PDF

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.

1.: Gérard R. and Tahara H., Solutions holomorphes et singulières d'équations aux dérivées partielles singulières non linéaires, Publ. Res. Inst. Math. Sci., 29(1993), 121-151. MR 1208031 (94h:35005)
2.: Gérard R. and Tahara H., ``Singular nonlinear partial differential equations'', Vieweg, Bonn. (1996) MR 1757086 (2001c:35056)
3.: Kobayashi T., Singular solutions and prolongation of holomorphic solutions to nonlinear differential equations, Publ. RIMS, Kyoto Univ., 34(1998), 43-63. MR 1617617 (99c:35004)
4.: Kichenassamy S. and Littman W., Blow-up surfaces for nonlinear wave equations, I, Comm. Partial Differential Equations, 18(3&4)(1993), 431-452. MR 1214867 (94f:35087)
5.: Kichenassamy S. and Littman W., Blow-up surfaces for nonlinear wave equations, II, Comm. Partial Differential Equations, 18(11)(1993), 1869-1899. MR 1243529 (94m:35197)
6.: Kichenassamy S. and Srinivasan G. K., The structure of WTC expansions and applications, J. Phys. A: Math. Gen., 28(1995), 1977-2004. MR 1336507 (96c:35029)
7.: Tahara H., On the singularities of solutions of nonlinear partial differential equations in the complex domain, ``Microlocal Analysis and Complex Fourier Analysis'', World Sci. Publ., Hackensack, NJ (2002), 273-283. MR 2068543 (2005b:35005)
8.: Tahara H., On the singularities of solutions of nonlinear partial differential equations in the complex domain, II, ``Differential equations & asymptotic theory in mathematical physics'', Ser. Anal. 2, World Sci. Publ., Hackensack, NJ (2004), 343-354. MR 2161979 (2006d:35030)
9.: Uchikoshi K., Singular Cauchy problems for quasilinear equations of order two, J. Math. Pures Appl. (9) 83(9)(2004), 1151-1178. MR 2091958 (2005k:35006)
10.: Yamane H., Nonlinear Cauchy problems with small analytic data, Proc. Amer. Math. Soc. 134(11)(2006), 3353-3361. MR 2231920

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 35L70, 35A20

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: 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
Posted: 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
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6826 (e) ISSN 0002-9939 (p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2009, American Mathematical Society Privacy Statement		Search the AMS