Document Type

Article

Publication Date

2019

Abstract

In this paper, we study a generalized Camassa–Holm (gCH) model with both dissipation and dispersion, which has (N+1)-order nonlinearities and includes the following three integrable equations: the Camassa–Holm, the Degasperis–Procesi, and the Novikov equations, as its reductions. We first present the local well-posedness and a precise blow-up scenario of the Cauchy problem for the gCH equation. Then, we provide several sufficient conditions that guarantee the global existence of the strong solutions to the gCH equation. Finally, we investigate the propagation speed for the gCH equation when the initial data are compactly supported.

Comments

© 2019 Springer Nature Switzerland AG. Original published version available at https://doi.org/10.1007/s00028-019-00533-5

First Page

403

Last Page

419

Publication Title

Journal of Evolution Equations

DOI

10.1007/s00028-019-00533-5

Included in

Mathematics Commons

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