Nonlinear Cauchy problems with small analytic data
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- by Hideshi Yamane PDF
- Proc. Amer. Math. Soc. 134 (2006), 3353-3361 Request permission
Abstract:
We study the lifespan of solutions to fully nonlinear Cauchy problems with small real- or complex-analytic data. Our proofs are based on the method of majorants and the fixed point theorem for a contraction mapping.References
- P. D’Ancona and S. Spagnolo, Global solvability for the degenerate Kirchhoff equation with real analytic data, Invent. Math. 108 (1992), no. 2, 247–262. MR 1161092, DOI 10.1007/BF02100605
- Vladimir Georgiev, Semilinear hyperbolic equations, MSJ Memoirs, vol. 7, Mathematical Society of Japan, Tokyo, 2000. With a preface by Y. Shibata. MR 1807081
- Daniel Gourdin and Mustapha Mechab, Problème de Cauchy pour des équations de Kirchhoff généralisées, Comm. Partial Differential Equations 23 (1998), no. 5-6, 761–776 (French, with English summary). MR 1632815, DOI 10.1080/03605309808821364
- Lars Hörmander, Lectures on nonlinear hyperbolic differential equations, Mathématiques & Applications (Berlin) [Mathematics & Applications], vol. 26, Springer-Verlag, Berlin, 1997. MR 1466700
- Satyanad Kichenassamy, Nonlinear wave equations, Monographs and Textbooks in Pure and Applied Mathematics, vol. 194, Marcel Dekker, Inc., New York, 1996. MR 1362547
- Claude Wagschal, Le problème de Goursat non linéaire, J. Math. Pures Appl. (9) 58 (1979), no. 3, 309–337 (French). MR 544256
- Seiichiro Wakabayashi, The Lax-Mizohata theorem for nonlinear Cauchy problems, Comm. Partial Differential Equations 26 (2001), no. 7-8, 1367–1384. MR 1855282, DOI 10.1081/PDE-100106137
Additional Information
- Hideshi Yamane
- Affiliation: Department of Physics, Kwansei Gakuin University, Gakuen 2-1, Sanda, Hyougo 669-1337, Japan
- MR Author ID: 605525
- Email: yamane@ksc.kwansei.ac.jp
- Received by editor(s): November 23, 2004
- Received by editor(s) in revised form: June 6, 2005
- Published electronically: May 12, 2006
- Communicated by: David S. Tartakoff
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 3353-3361
- MSC (2000): Primary 35A05, 35L70
- DOI: https://doi.org/10.1090/S0002-9939-06-08410-3
- MathSciNet review: 2231920