Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A sharp condition for the well-posedness of the linear KdV-type equation

Author: Timur Akhunov
Journal: Proc. Amer. Math. Soc. 142 (2014), 4207-4220
MSC (2010): Primary 35Q53
Published electronically: August 7, 2014
MathSciNet review: 3266990
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: An initial value problem for a very general linear equation of KdV-type is considered. Assuming non-degeneracy of the third derivative coefficient, this problem is shown to be well-posed under a certain simple condition, which is an adaptation of the Mizohata-type condition from the Schrödinger equation to the context of KdV. When this condition is violated, ill-posedness is shown by an explicit construction. These results justify formal heuristics associated with dispersive problems and have applications to non-linear problems of KdV-type.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 35Q53

Retrieve articles in all journals with MSC (2010): 35Q53

Additional Information

Timur Akhunov
Affiliation: Department of Mathematics, University of Calgary, 2500 University Drive NW, Calgary, Alberta, T2N 1N4, Canada
Address at time of publication: Department of Mathematics, 820 Hylan Building, University of Rochester, Rochester, New York 14627

Keywords: KdV, linear, dispersive, partial differential equations, energy method, Mizohata condition
Received by editor(s): October 11, 2012
Received by editor(s) in revised form: January 9, 2013
Published electronically: August 7, 2014
Communicated by: Joachim Krieger
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society