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Research Article | Open Access

The entropy weak solution to a nonlinear shallow water wave equation including the Degasperis-Procesi model

Mingming Li1, Shaoyong Lai2( )
School of Mathematics and Statistics, Kashi University, Kashi, 844006, China
School of Mathematics, Southwestern University of Finance and Economics, Chengdu, 611130, China
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Abstract

A nonlinear model, which characterizes motions of shallow water waves and includes the famous Degasperis-Procesi equation, is considered. The essential step is the derivation of the L 2 ( R ) uniform bound of solutions for the nonlinear model if its initial value belongs to space L 2 ( R ). Utilizing the bounded property leads to several estimates about its solutions. The viscous approximation technique is employed to establish the well-posedness of entropy weak solutions.

Keywords

Entropy solutionshallow water wave modelexistence and uniqueness
CLC number: 35Q35, 76B25

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AIMS Mathematics
Volume 9 Issue 1,
January 2024
Pages 1772-1782
DOI: 10.3934/math.2024086

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Cite this article:
Li M, Lai S. The entropy weak solution to a nonlinear shallow water wave equation including the Degasperis-Procesi model. AIMS Mathematics, 2024, 9(1): 1772-1782. https://doi.org/10.3934/math.2024086

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Received: 24 October 2023
Revised: 18 November 2023
Accepted: 22 November 2023
Published: 15 January 2024
©2024 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)