Several dynamical properties for a nonlinear shallow water equation (Q1717795)
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scientific article; zbMATH DE number 7015820
| Language | Label | Description | Also known as |
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| English | Several dynamical properties for a nonlinear shallow water equation |
scientific article; zbMATH DE number 7015820 |
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Several dynamical properties for a nonlinear shallow water equation (English)
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8 February 2019
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Summary: A nonlinear third order dispersive shallow water equation including the Degasperis-Procesi model is investigated. The existence of weak solutions for the equation is proved in the space \(L^1(\mathbb R) \cap B V(\mathbb R)\) under certain assumptions. The Oleinik type estimate and \(L^{2 N}(\mathbb R)\) (\(N\) is a natural number) estimate for the solution are obtained.
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