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期刊名称: Nonlinearity
Volume:25    Issue:2        Page:449-479
ISSN:0951-7715

The Cauchy problem for the Novikov equation期刊论文

作者: Himonas A Alexandrou Holliman Curtis
DOI:10.1088/0951-7715/25/2/449

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页码: 449-479
被引频次: 98
出版者: IOP Publishing,IOP PUBLISHING LTD
期刊名称: Nonlinearity
ISSN: 0951-7715
卷期: Volume:25    Issue:2
语言: English
摘要: This work studies the initial value problem for a Camassa-Holm type equation with cubic nonlinearities that has been recently discovered by Vladimir Novikov to be integrable. For s > 3/2, using a Galerkin-type approximation method, it is shown that this equation is well-posed in Sobolev spaces H-s on both the line and the circle with continuous dependence on initial data. Furthermore, it is proved that this dependence is optimal by showing that the data-to-solution map is not uniformly continuous. The nonuniform dependence is proved using the method of approximate solutions in conjunction with well-posedness estimates.
相关主题: PEAKON, MATHEMATICS, APPLIED, NONUNIFORM DEPENDENCE, WELL-POSEDNESS, ILL-POSEDNESS, PHYSICS, MATHEMATICAL, INTEGRABLE EQUATION,

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