The initial value problem for a third order dispersive equation on the two-dimensional torus
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- by Hiroyuki Chihara PDF
- Proc. Amer. Math. Soc. 133 (2005), 2083-2090 Request permission
Abstract:
We present the necessary and sufficient conditions for the $L^2$-well-posedness of the initial problem for a third order linear dispersive equation on the two-dimensional torus. Birkhoff’s method of asymptotic solutions is used to prove necessity. Some properties of a system for quadratic algebraic equations associated to the principal symbol play a crucial role in proving sufficiency.References
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Additional Information
- Hiroyuki Chihara
- Affiliation: Mathematical Institute, Tohoku University, Sendai 980-8578, Japan
- MR Author ID: 026745
- ORCID: 0000-0003-1491-7103
- Email: chihara@math.tohoku.ac.jp
- Received by editor(s): March 16, 2004
- Published electronically: January 31, 2005
- Communicated by: David S. Tartakoff
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 133 (2005), 2083-2090
- MSC (2000): Primary 35G10
- DOI: https://doi.org/10.1090/S0002-9939-05-07783-X
- MathSciNet review: 2137875