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

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

Nonlinear Analysis, Theory, Methods and Applications, cilt.75, sa.13, ss.4821-4838, 2012 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 75 Sayı: 13
  • Basım Tarihi: 2012
  • Doi Numarası: 10.1016/j.na.2012.03.031
  • Dergi Adı: Nonlinear Analysis, Theory, Methods and Applications
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.4821-4838
  • Anahtar Kelimeler: b-family, Non-uniform continuity, Traveling wave
  • Trakya Üniversitesi Adresli: Hayır

Özet

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.