$ L^1 $ local stability to a nonlinear shallow water wave model
A nonlinear shallow water wave equation containing the famous Degasperis$ - $Procesi and Fornberg$ - $Whitham models is investigated. The novel derivation is that we establish the $ L^2 $ bounds of solutions from the equation if its initial value belongs to space $ L^2(\mathbb{R}) $. The $ L^{\infty...
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| Language: | English |
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AIMS Press
2024-09-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2024251 |
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| author | Jun Meng Shaoyong Lai |
| author_facet | Jun Meng Shaoyong Lai |
| author_sort | Jun Meng |
| collection | DOAJ |
| description | A nonlinear shallow water wave equation containing the famous Degasperis$ - $Procesi and Fornberg$ - $Whitham models is investigated. The novel derivation is that we establish the $ L^2 $ bounds of solutions from the equation if its initial value belongs to space $ L^2(\mathbb{R}) $. The $ L^{\infty} $ bound of the solution is derived. The techniques of doubling the space variable are employed to set up the $ L^1 $ local stability of short time solutions. |
| format | Article |
| id | doaj-art-b40510c5923d4d8788f949972183aaa2 |
| institution | Kabale University |
| issn | 2688-1594 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj-art-b40510c5923d4d8788f949972183aaa22025-01-23T07:52:42ZengAIMS PressElectronic Research Archive2688-15942024-09-013295409542310.3934/era.2024251$ L^1 $ local stability to a nonlinear shallow water wave modelJun Meng0Shaoyong Lai1School of Mathematics and Statistics, Kashi University, Kashi 844006, ChinaSchool of Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, ChinaA nonlinear shallow water wave equation containing the famous Degasperis$ - $Procesi and Fornberg$ - $Whitham models is investigated. The novel derivation is that we establish the $ L^2 $ bounds of solutions from the equation if its initial value belongs to space $ L^2(\mathbb{R}) $. The $ L^{\infty} $ bound of the solution is derived. The techniques of doubling the space variable are employed to set up the $ L^1 $ local stability of short time solutions.https://www.aimspress.com/article/doi/10.3934/era.2024251local strong solutionsbounds of solutionshallow water wave model$ l^1 $ local stability |
| spellingShingle | Jun Meng Shaoyong Lai $ L^1 $ local stability to a nonlinear shallow water wave model Electronic Research Archive local strong solutions bounds of solution shallow water wave model $ l^1 $ local stability |
| title | $ L^1 $ local stability to a nonlinear shallow water wave model |
| title_full | $ L^1 $ local stability to a nonlinear shallow water wave model |
| title_fullStr | $ L^1 $ local stability to a nonlinear shallow water wave model |
| title_full_unstemmed | $ L^1 $ local stability to a nonlinear shallow water wave model |
| title_short | $ L^1 $ local stability to a nonlinear shallow water wave model |
| title_sort | l 1 local stability to a nonlinear shallow water wave model |
| topic | local strong solutions bounds of solution shallow water wave model $ l^1 $ local stability |
| url | https://www.aimspress.com/article/doi/10.3934/era.2024251 |
| work_keys_str_mv | AT junmeng l1localstabilitytoanonlinearshallowwaterwavemodel AT shaoyonglai l1localstabilitytoanonlinearshallowwaterwavemodel |