The Cauchy problem to a gkCH equation with peakon solutions

Yunxi Guo; Ying Wang; Yunxi Guo; Ying Wang

doi:10.3934/math.2022707

AIMS Mathematics

2022, Volume 7, Issue 7: 12781-12801. doi: 10.3934/math.2022707

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The Cauchy problem to a gkCH equation with peakon solutions

Yunxi Guo ^,,
Ying Wang

Department of Mathematics, Zunyi Normal University, Zunyi 563006, China

Received: 07 March 2022 Revised: 02 April 2022 Accepted: 15 April 2022 Published: 05 May 2022
MSC : 35D05, 35G25, 35L05, 35Q35

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^{2k} $ estimate plays a crucial role. In addition, we also show that peakon solutions are global weak solutions.
- $ L^{2k} $ estimate,
- blow-up solutions,
- blow-up phenomena,
- peakon solutions,
- generalized Camassa-Holm equation
Citation: Yunxi Guo, Ying Wang. The Cauchy problem to a gkCH equation with peakon solutions[J]. AIMS Mathematics, 2022, 7(7): 12781-12801. doi: 10.3934/math.2022707

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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^{2k} $ estimate plays a crucial role. In addition, we also show that peakon solutions are global weak solutions.

References

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