Global existence of weak solutions for a shallow water equation

Global existence of weak solutions for a shallow water equation

A nonlinear shallow water equation, which includes the famous Camassa–Holm (CH) and Degasperis–Procesi (DP) equations as special cases, is investigated. Provided that initial value u 0 ∈ H s ( 1 ≤ s ≤ 3 2 ) , u 0 ∈ L 1 ( R ) and ( 1 − ∂ x 2 ) u 0 does not change sign, it is shown that there exists a...

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Veröffentlicht in:Computers & mathematics with applications (1987) 2010-11, Vol.60 (9), p.2645-2652
Hauptverfasser: Yin, Zheng, Lai, Shaoyong, Guo, Yunxi
Format: Artikel
Sprache:eng
Schlagworte:
Blow-up
Global existence
Local well-posedness
Mathematical analysis
Mathematical models
Nonlinearity
Shallow water equations
Shallow water model
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Zusammenfassung:A nonlinear shallow water equation, which includes the famous Camassa–Holm (CH) and Degasperis–Procesi (DP) equations as special cases, is investigated. Provided that initial value u 0 ∈ H s ( 1 ≤ s ≤ 3 2 ) , u 0 ∈ L 1 ( R ) and ( 1 − ∂ x 2 ) u 0 does not change sign, it is shown that there exists a unique global weak solution to the equation.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2010.08.094