Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 397, Issue 2, Pages 515-521Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2012.08.006
Keywords
Novikov; Peakon solutions; Integrable; Sobolev spaces; Initial value problem; Non-uniform dependence on initial data
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We consider both the periodic and the non-periodic Cauchy problem for the Novikov equation and discuss continuity results for the data-to-solution map in Sobolev spaces. In particular, we show that the data-to-solution map is not (globally) uniformly continuous in Sobolev spaces with exponent less than 3/2. To accomplish this, we construct sequences of peakon solutions whose distance initially goes to zero but later becomes large. (C) 2012 Elsevier Inc. All rights reserved.
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