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

DOI:
https://doi.org/10.1090/S0002-9939-05-07783-X

Published electronically:
January 31, 2005

MathSciNet review:
2137875

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Abstract: We present the necessary and sufficient conditions for the -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.