The Local and Global Existence of Solutions for a Generalized Camassa-Holm Equation
Keyword(s):
A nonlinear generalization of the Camassa-Holm equation is investigated. By making use of the pseudoparabolic regularization technique, its local well posedness in Sobolev spaceHS(R)withs>3/2is established via a limiting procedure. Provided that the initial valueu0satisfies the sign condition andu0∈Hs(R) (s>3/2), it is shown that there exists a unique global solution for the equation in spaceC([0,∞);Hs(R))∩C1([0,∞);Hs−1(R)).
2019 ◽
Vol 26
(1/2)
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pp. 127-152
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2016 ◽
Vol 13
(02)
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pp. 381-415
2001 ◽
Vol 43
(3)
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pp. 293-323
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2004 ◽
Vol 21
(5)
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pp. 1035-1044
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2004 ◽
Vol 21
(4)
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pp. 881-892
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2012 ◽
Vol 09
(03)
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pp. 451-467
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