Global well-posedness and infinite propagation speed for the N−abc family of Camassa–Holm type equation with both dissipation and dispersion
Global well-posedness and infinite propagation speed for the N−abc family of Camassa–Holm type equation with both dissipation and dispersion
复制标题
具有耗散和色散的 Camassa-Holm 型方程 N - abc 族的全局适定性和无限传播速度
DOI：
10.1063/5.0010374
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发表时间：
2020
影响因子：
1.3
通讯作者：
Wen Zhu
中科院分区：
文献类型：
--
作者：
Zaiyun Zhang;Zhenhai Liu;Youjun Deng;Chuangxia Huang;Shi-you Lin;Wen Zhu
本文考虑了具有耗散和色散的Camassa-Holm型方程N-abc族的Cauchy问题.首先，我们在一定条件下，在初始数据上建立了强解的整体适定性。然后，我们研究的传播速度与compatible支持的初始数据。该结果改进了文献中报道的早期结果，例如Novruzov等人的结果[J. Differ.方程式257，4525-4541（2014）]，Hwang和Moon [Electron.Res.Arch.28（1），15-25（2020）]，以及Himonas和Thompson [J.Math.Phys.55，091503（2014）]。
In this paper, we consider the Cauchy problem for the N−abc family of the Camassa–Holm type equation with both dissipation and dispersion. First, we establish the global well-posedness of the strong solutions under certain conditions on the initial datum. Then, we investigate the propagation speed with compactly supported initial data. This result improves earlier ones reported in the literature, such as those by Novruzov et al. [J. Differ. Equations 257, 4525–4541 (2014)], Hwang and Moon [Electron. Res. Arch. 28(1), 15–25 (2020)], and Himonas and Thompson [J. Math. Phys. 55, 091503 (2014)].