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March/April 2009 Non-uniform dependence on initial data for the CH equation on the line
A. Alexandrou Himonas, Carlos Kenig
Differential Integral Equations 22(3/4): 201-224 (March/April 2009).

Abstract

For $s > 1$ two sequences of CH solutions living in a bounded subset of the Sobolev space $H^s(\mathbb{R})$ are constructed, whose distance at the initial time is converging to zero while at any later time it is bounded below by a positive constant. This implies that the solution map of the CH equation is not uniformly continuous in $H^s(\mathbb{R})$.

Citation

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A. Alexandrou Himonas. Carlos Kenig. "Non-uniform dependence on initial data for the CH equation on the line." Differential Integral Equations 22 (3/4) 201 - 224, March/April 2009.

Information

Published: March/April 2009
First available in Project Euclid: 20 December 2012

zbMATH: 1240.35242
MathSciNet: MR2492817

Subjects:
Primary: 35Q53

Rights: Copyright © 2009 Khayyam Publishing, Inc.

JOURNAL ARTICLE
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Vol.22 • No. 3/4 • March/April 2009
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