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The entropy weak solution to a generalized Fornberg–Whitham equation
Boundary Value Problems ( IF 1.7 ) Pub Date : 2020-05-24 , DOI: 10.1186/s13661-020-01400-w
Nan Li , Shaoyong Lai

We investigate a nonlinear generalized Fornberg–Whitham equation. The key element is that we derive an $L^{2}(\mathbb{R})$ conservation law for solutions of the equation. We establish several estimates by utilizing the $L^{2}(\mathbb{R})$ conservation law. These estimates lead to the proof of the existence and uniqueness of entropy weak solution of the equation in the space $L^{1}(\mathbb{R})\cap L^{\infty}(\mathbb{R})$.

中文翻译:

广义Fornberg-Whitham方程的熵弱解

我们研究了非线性广义Fornberg-Whitham方程。关键因素是我们导出了方程的解的L ^ {2}(\ mathbb {R})$守恒律。我们利用$ L ^ {2}(\ mathbb {R})$守恒定律建立了几个估计。这些估计导致证明了在空间$ L ^ {1}(\ mathbb {R})\ cap L ^ {\ infty}(\ mathbb {R})$中方程的熵弱解的存在和唯一性。
更新日期:2020-05-24
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