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Indexed by:期刊论文

Date of Publication:2018-10-01

Journal:NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS

Included Journals:SCIE

Volume:175

Page Number:210-236

ISSN No.:0362-546X

Key Words:Higher-order mu-Camassa-Holm equation; Global existence; Weak solutions; Holder continuity; Peakon solutions

Abstract:In this paper, we study the Cauchy problem of a higher-order mu-Camassa-Holm equation. By employing the Green's function of (mu - partial derivative(2)(x))(-2), we obtain the explicit formula of the inverse function (mu-partial derivative(2)(x))(-2)w and local well-posedness for the equation in Sobolev spaces H-s(S), s > 7/2. Then we prove the existence of global strong solutions and weak solutions. Moreover, we show that the data-to-solution map is Holder continuous in Hs(S), s >= 4, equipped with the H-r(S)-topology for 0 <= r < s. Finally, the equation is shown to admit single peakon solutions which have continuous second derivatives and jump discontinuities in the third derivatives. (C) 2018 Elsevier Ltd. All rights reserved.