Global well-posedness and infinite propagation speed for the N − abc family of Camassa–Holm type equation with both dissipation and dispersion
| Autor: | Wen Zhu, Shiyou Lin, Zhenhai Liu, Youjun Deng, Zaiyun Zhang, Chuangxia Huang |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Physics
010102 general mathematics Mathematical analysis Geodetic datum Statistical and Nonlinear Physics Electron Dissipation 01 natural sciences Type equation 0103 physical sciences Dispersion (optics) Initial value problem 010307 mathematical physics 0101 mathematics Arch Mathematical Physics Well posedness |
| Zdroj: | Journal of Mathematical Physics. 61:071502 |
| ISSN: | 1089-7658 0022-2488 |
| DOI: | 10.1063/5.0010374 |
| Popis: | 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)]. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|