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Research Article | Open Access

Blow-up to a shallow water wave model including the Degasperis-Procesi equation

Jin Hong1( ), Shaoyong Lai2
School of Mathematics and Statistics, Yili Normal University, Yili 835000, China
School of Mathematics, Southwestern University of Finance and Economics, Chengdu 610030, China
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Abstract

A nonlinear equation, depicting motions of shallow water waves and including the famous Degasperis-Procesi model, is considered. The key element is that we derive L 2 conservation law of solutions for the nonlinear equation, which leads to the bound of the solution itself. Using several estimates derived from the model, we obtain that when its solution blows up in the Sobolev space if and only if the space derivative of the solution tends to minus infinite.

Keywords

blow upshallow water wave equationgeneralized Degasperis-Procesi modelclassical energy methods
CLC number: 35G25, 35L05

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AIMS Mathematics
Volume 8 Issue 11,
November 2023
Pages 25409-25421
DOI: 10.3934/math.20231296

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Cite this article:
Hong J, Lai S. Blow-up to a shallow water wave model including the Degasperis-Procesi equation. AIMS Mathematics, 2023, 8(11): 25409-25421. https://doi.org/10.3934/math.20231296

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Received: 04 June 2023
Revised: 31 July 2023
Accepted: 22 August 2023
Published: 15 November 2023
©2023 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)