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Research Article | Open Access

The Cauchy problem to a gkCH equation with peakon solutions

Yunxi Guo( ), Ying Wang
Department of Mathematics, Zunyi Normal University, Zunyi 563006, China
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Abstract

Considered in this paper is a generalized Camassa-Holm equation, which includes both the Camassa-Holm equation and the Novikov equation as two special cases. Firstly, two blow-up criteria are established for the generalized Camassa-Holm equation. Then we derive two blow-up phenomena, where a new L 2 k estimate plays a crucial role. In addition, we also show that peakon solutions are global weak solutions.

Keywords

L2k estimateblow-up solutionsblow-up phenomenapeakon solutionsgeneralized Camassa-Holm equation
CLC number: 35D05, 35G25, 35L05, 35Q35

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AIMS Mathematics
Volume 7 Issue 7,
July 2022
Pages 12781-12801
DOI: 10.3934/math.2022707

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Cite this article:
Guo Y, Wang Y. The Cauchy problem to a gkCH equation with peakon solutions. AIMS Mathematics, 2022, 7(7): 12781-12801. https://doi.org/10.3934/math.2022707

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Received: 07 March 2022
Revised: 02 April 2022
Accepted: 15 April 2022
Published: 15 July 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)