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- Title
LIOUVILLE THEOREMS FOR PERIODIC TWO-COMPONENT SHALLOW WATER SYSTEMS.
- Authors
Hu, Qiaoyi; Wu, Zhixin; Sun, Yumei
- Abstract
We establish Liouville-type theorems for periodic two-component shallow water systems, including a two-component Camassa-Holm equation (2CH) and a two-component Degasperis-Procesi (2DP) equation. More presicely, we prove that the only global, strong, spatially periodic solutions to the equa- tions, vanishing at some point (t0; x0), are the identically zero solutions. Also, we derive new local-in-space blow-up criteria for the dispersive 2CH and 2DP.
- Subjects
CAUCHY problem; NONLINEAR equations; WAVE equation; FRACTIONAL calculus; INVARIANT wave equations
- Publication
Discrete & Continuous Dynamical Systems: Series A, 2018, Vol 38, Issue 6, p3085
- ISSN
1078-0947
- Publication type
Article
- DOI
10.3934/dcds.2018134