Blow-up solution and analyticity to a generalized Camassa-Holm equation

Ying Wang; Yunxi Guo; Ying Wang; Yunxi Guo

doi:10.3934/math.2023544

AIMS Mathematics

2023, Volume 8, Issue 5: 10728-10744. doi: 10.3934/math.2023544

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Blow-up solution and analyticity to a generalized Camassa-Holm equation

Ying Wang ,
Yunxi Guo ^,

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

Received: 15 December 2022 Revised: 14 February 2023 Accepted: 22 February 2023 Published: 03 March 2023
MSC : 35D05, 35G25, 35L05, 35Q35

A generalized Camassa-Holm equation with higher order nonlinear term was studied. First, we give a new blow-up criterion and a new blow-up phenomenon to the Cauchy problem for the equation under some conditions. Then, we focus on the analytical solutions for the equation. Finally, we prove the analyticity of solution for the equation.
- blow-up criterion,
- blow-up phenomenon,
- analytical solutions,
- analyticity,
- a generalized Camassa-Holm equation
Citation: Ying Wang, Yunxi Guo. Blow-up solution and analyticity to a generalized Camassa-Holm equation[J]. AIMS Mathematics, 2023, 8(5): 10728-10744. doi: 10.3934/math.2023544

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Abstract

A generalized Camassa-Holm equation with higher order nonlinear term was studied. First, we give a new blow-up criterion and a new blow-up phenomenon to the Cauchy problem for the equation under some conditions. Then, we focus on the analytical solutions for the equation. Finally, we prove the analyticity of solution for the equation.

References

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