The entropy weak solution to a nonlinear shallow water wave equation including the Degasperis-Procesi model
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(\mathbb{R}) $ uniform bound of solutions for the nonlinear model if its initial value belongs to space $ L^2(\ma...
| Published in: | AIMS Mathematics |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2024-01-01
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| Online Access: | https://aimspress.com/article/doi/10.3934/math.2024086?viewType=HTML |
| _version_ | 1850003622042009600 |
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| author | Mingming Li Shaoyong Lai |
| author_facet | Mingming Li Shaoyong Lai |
| author_sort | Mingming Li |
| collection | DOAJ |
| container_title | AIMS Mathematics |
| description | 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(\mathbb{R}) $ uniform bound of solutions for the nonlinear model if its initial value belongs to space $ L^2(\mathbb{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. |
| format | Article |
| id | doaj-art-cdcdb3c3222e4e89a36ca8327e2f37bf |
| institution | Directory of Open Access Journals |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| spelling | doaj-art-cdcdb3c3222e4e89a36ca8327e2f37bf2025-08-20T00:47:58ZengAIMS PressAIMS Mathematics2473-69882024-01-01911772178210.3934/math.2024086The entropy weak solution to a nonlinear shallow water wave equation including the Degasperis-Procesi modelMingming Li0Shaoyong Lai11. School of Mathematics and Statistics, Kashi University, Kashi, 844006, China2. School of Mathematics, Southwestern University of Finance and Economics, Chengdu, 611130, ChinaA 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(\mathbb{R}) $ uniform bound of solutions for the nonlinear model if its initial value belongs to space $ L^2(\mathbb{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.https://aimspress.com/article/doi/10.3934/math.2024086?viewType=HTMLentropy solutionshallow water wave modelexistence and uniqueness |
| spellingShingle | Mingming Li Shaoyong Lai The entropy weak solution to a nonlinear shallow water wave equation including the Degasperis-Procesi model entropy solution shallow water wave model existence and uniqueness |
| title | The entropy weak solution to a nonlinear shallow water wave equation including the Degasperis-Procesi model |
| title_full | The entropy weak solution to a nonlinear shallow water wave equation including the Degasperis-Procesi model |
| title_fullStr | The entropy weak solution to a nonlinear shallow water wave equation including the Degasperis-Procesi model |
| title_full_unstemmed | The entropy weak solution to a nonlinear shallow water wave equation including the Degasperis-Procesi model |
| title_short | The entropy weak solution to a nonlinear shallow water wave equation including the Degasperis-Procesi model |
| title_sort | entropy weak solution to a nonlinear shallow water wave equation including the degasperis procesi model |
| topic | entropy solution shallow water wave model existence and uniqueness |
| url | https://aimspress.com/article/doi/10.3934/math.2024086?viewType=HTML |
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