Release Time:2019-03-12  Hits:

Indexed by: Journal Article

Date of Publication: 2018-10-01

Journal: NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS

Included Journals: SCIE

Volume: 175

Page Number: 210-236

ISSN: 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.