$ 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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2024-09-01
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| Series: | Electronic Research Archive |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2024251 |
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| Summary: | 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. |
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| ISSN: | 2688-1594 |