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Non‐uniform dependence and persistence properties for coupled Camassa–Holm equations
Author(s) -
Zhou Shouming
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4258
Subject(s) - camassa–holm equation , persistence (discontinuity) , mathematics , sobolev space , initial value problem , mathematical analysis , cauchy problem , integrable system , geotechnical engineering , engineering
This paper deals with the non‐uniform dependence and persistence properties for a coupled Camassa–Holm equations. Using the method of approximate solutions in conjunction with well‐posedness estimate, it is proved that the solution map of the Cauchy problem for this coupled Camassa–Holm equation is not uniformly continuous in Sobolev spaces H s with s > 3/2. On the other hand, the persistence properties in weighted L p spaces for the solution of this coupled Camassa–Holm system are considered. Copyright © 2016 John Wiley & Sons, Ltd.