AI Chat Paper
Note: Please note that the following content is generated by AMiner AI. SciOpen does not take any responsibility related to this content.
{{lang === 'zh_CN' ? '文章概述' : 'Summary'}}
{{lang === 'en_US' ? '中' : 'Eng'}}
Chat more with AI
Powered by AMiner. Clicking this button will take you away from SciOpen.
Home AIMS Mathematics Article
PDF (231.2 KB)
Cite
EndNote(RIS) BibTeX
Collect
Submit Manuscript AI Chat Paper
Show Outline
Outline
Show full outline
Hide outline
Outline
Show full outline
Hide outline
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
Show Author Information

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

References

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

{{item.num}}

Comments on this article

Go to comment

< Back to all reports

Review Status: {{reviewData.commendedNum}} Commended , {{reviewData.revisionRequiredNum}} Revision Required , {{reviewData.notCommendedNum}} Not Commended Under Peer Review

Review Comment

Cite this Report
Close
Close
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

8

Views

0

Downloads

0

Crossref

0

Web of Science

0

Scopus
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)