Differential and Integral Equations

Non-uniform dependence on initial data for a family of non-linear evolution equations

Erika A. Olson

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Abstract

We show that solutions to the periodic Cauchy problem for a family of non-linear evolution equations, which contains the Camassa-Holm equation, do not depend uniformly continuously on initial data in the Sobolev space $H^s(\mathbb{T})$, when $s=1$ or $s\geq 2$.

Article information

Source
Differential Integral Equations, Volume 19, Number 10 (2006), 1081-1102.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356050310

Mathematical Reviews number (MathSciNet)
MR2278671

Zentralblatt MATH identifier
1212.35426

Subjects
Primary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10]
Secondary: 35B10: Periodic solutions 35B35: Stability

Citation

Olson, Erika A. Non-uniform dependence on initial data for a family of non-linear evolution equations. Differential Integral Equations 19 (2006), no. 10, 1081--1102. https://projecteuclid.org/euclid.die/1356050310


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