期刊
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
卷 95, 期 -, 页码 499-529出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.na.2013.09.028
关键词
Fokas; Olver; Rosenau; Qiao equation; Peakon; Travelling waves; Novikov equation; Integrable equations; Cubic nonlinearities; Cauchy problem; Sobolev spaces; Well-posedness; Non-uniform dependence on initial data; Approximate solutions; Commutator estimate; Conserved quantities
资金
- Simons Foundation [246116]
It is shown that the initial value problem for the Fokas-Olver-Rosenau-Qiao equation (FORQ) is well-posed in Sobolev spaces H-s, s > 5/2, in the sense of Hadamard. Furthermore, it is proved that the dependence on initial data is sharp, i.e. the data-to-solution map is continuous but not uniformly continuous. Also, peakon travelling wave solutions are derived on both the circle and the line and are used to prove that the solution map is not uniformly continuous in H-s for s < 3/2. (C) 2013 Elsevier Ltd. All rights reserved.
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