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The initial value problem for a third order dispersive equation on the two-dimensional torus


Author: Hiroyuki Chihara
Journal: Proc. Amer. Math. Soc. 133 (2005), 2083-2090
MSC (2000): Primary 35G10
Published electronically: January 31, 2005
MathSciNet review: 2137875
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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.


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Additional Information

Hiroyuki Chihara
Affiliation: Mathematical Institute, Tohoku University, Sendai 980-8578, Japan
Email: chihara@math.tohoku.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-05-07783-X
Received by editor(s): March 16, 2004
Published electronically: January 31, 2005
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.