Non-uniform continuity of periodic Holm-Staley b-family of equations

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Christov O., HAKKAEV S. A., Iliev I. D.

Nonlinear Analysis, Theory, Methods and Applications, vol.75, no.13, pp.4821-4838, 2012 (SCI-Expanded, Scopus)

• Publication Type: Article / Article
• Volume: 75 Issue: 13
• Publication Date: 2012
• Doi Number: 10.1016/j.na.2012.03.031
• Journal Name: Nonlinear Analysis, Theory, Methods and Applications
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Page Numbers: pp.4821-4838
• Keywords: b-family, Non-uniform continuity, Traveling wave
• Trakya University Affiliated: No

Abstract

We consider a family of non-evolutionary partial differential equations known as the Holm-Staley b-family which includes the integrable Camassa-Holm and Degasperis-Procesi equations. We show that the solution map is not uniformly continuous. The proof relies on a construction of smooth periodic traveling waves with small amplitude. © 2012 Elsevier Ltd. All rights reserved.