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Dissipative solutions for the Camassa-Holm equation
| 1. | Department of Mathematical Sciences, Norwegian University of Science and Technology, NO-7491 Trondheim |
| 2. | Department of Mathematical Sciences, Norwegian University of Science and Technology, NO--7491 Trondheim |
| [1] |
Katrin Grunert, Helge Holden, Xavier Raynaud. Lipschitz metric for the Camassa--Holm equation on the line. Discrete and Continuous Dynamical Systems, 2013, 33 (7) : 2809-2827. doi: 10.3934/dcds.2013.33.2809 |
| [2] |
Katrin Grunert, Helge Holden, Xavier Raynaud. Global conservative solutions to the Camassa--Holm equation for initial data with nonvanishing asymptotics. Discrete and Continuous Dynamical Systems, 2012, 32 (12) : 4209-4227. doi: 10.3934/dcds.2012.32.4209 |
| [3] |
Min Zhu, Shuanghu Zhang. On the blow-up of solutions to the periodic modified integrable Camassa--Holm equation. Discrete and Continuous Dynamical Systems, 2016, 36 (4) : 2347-2364. doi: 10.3934/dcds.2016.36.2347 |
| [4] |
Shouming Zhou, Chunlai Mu. Global conservative and dissipative solutions of the generalized Camassa-Holm equation. Discrete and Continuous Dynamical Systems, 2013, 33 (4) : 1713-1739. doi: 10.3934/dcds.2013.33.1713 |
| [5] |
Helge Holden, Xavier Raynaud. A convergent numerical scheme for the Camassa--Holm equation based on multipeakons. Discrete and Continuous Dynamical Systems, 2006, 14 (3) : 505-523. doi: 10.3934/dcds.2006.14.505 |
| [6] |
Xinglong Wu, Boling Guo. Persistence properties and infinite propagation for the modified 2-component Camassa--Holm equation. Discrete and Continuous Dynamical Systems, 2013, 33 (7) : 3211-3223. doi: 10.3934/dcds.2013.33.3211 |
| [7] |
Zhenhua Guo, Mina Jiang, Zhian Wang, Gao-Feng Zheng. Global weak solutions to the Camassa-Holm equation. Discrete and Continuous Dynamical Systems, 2008, 21 (3) : 883-906. doi: 10.3934/dcds.2008.21.883 |
| [8] |
Xinglong Wu. On the Cauchy problem of a three-component Camassa--Holm equations. Discrete and Continuous Dynamical Systems, 2016, 36 (5) : 2827-2854. doi: 10.3934/dcds.2016.36.2827 |
| [9] |
Katrin Grunert. Blow-up for the two-component Camassa--Holm system. Discrete and Continuous Dynamical Systems, 2015, 35 (5) : 2041-2051. doi: 10.3934/dcds.2015.35.2041 |
| [10] |
Yonghui Zhou, Shuguan Ji. Wave breaking phenomena and global existence for the weakly dissipative generalized Camassa-Holm equation. Communications on Pure and Applied Analysis, 2022, 21 (2) : 555-566. doi: 10.3934/cpaa.2021188 |
| [11] |
Stephen C. Anco, Elena Recio, María L. Gandarias, María S. Bruzón. A nonlinear generalization of the Camassa-Holm equation with peakon solutions. Conference Publications, 2015, 2015 (special) : 29-37. doi: 10.3934/proc.2015.0029 |
| [12] |
Li Yang, Zeng Rong, Shouming Zhou, Chunlai Mu. Uniqueness of conservative solutions to the generalized Camassa-Holm equation via characteristics. Discrete and Continuous Dynamical Systems, 2018, 38 (10) : 5205-5220. doi: 10.3934/dcds.2018230 |
| [13] |
Shihui Zhu. Existence and uniqueness of global weak solutions of the Camassa-Holm equation with a forcing. Discrete and Continuous Dynamical Systems, 2016, 36 (9) : 5201-5221. doi: 10.3934/dcds.2016026 |
| [14] |
Danping Ding, Lixin Tian, Gang Xu. The study on solutions to Camassa-Holm equation with weak dissipation. Communications on Pure and Applied Analysis, 2006, 5 (3) : 483-492. doi: 10.3934/cpaa.2006.5.483 |
| [15] |
Stephen Anco, Daniel Kraus. Hamiltonian structure of peakons as weak solutions for the modified Camassa-Holm equation. Discrete and Continuous Dynamical Systems, 2018, 38 (9) : 4449-4465. doi: 10.3934/dcds.2018194 |
| [16] |
Alberto Bressan, Geng Chen, Qingtian Zhang. Uniqueness of conservative solutions to the Camassa-Holm equation via characteristics. Discrete and Continuous Dynamical Systems, 2015, 35 (1) : 25-42. doi: 10.3934/dcds.2015.35.25 |
| [17] |
Shaoyong Lai, Qichang Xie, Yunxi Guo, YongHong Wu. The existence of weak solutions for a generalized Camassa-Holm equation. Communications on Pure and Applied Analysis, 2011, 10 (1) : 45-57. doi: 10.3934/cpaa.2011.10.45 |
| [18] |
Li Yang, Chunlai Mu, Shouming Zhou, Xinyu Tu. The global conservative solutions for the generalized camassa-holm equation. Electronic Research Archive, 2019, 27: 37-67. doi: 10.3934/era.2019009 |
| [19] |
Yongsheng Mi, Boling Guo, Chunlai Mu. Persistence properties for the generalized Camassa-Holm equation. Discrete and Continuous Dynamical Systems - B, 2020, 25 (5) : 1623-1630. doi: 10.3934/dcdsb.2019243 |
| [20] |
Yu Gao, Jian-Guo Liu. The modified Camassa-Holm equation in Lagrangian coordinates. Discrete and Continuous Dynamical Systems - B, 2018, 23 (6) : 2545-2592. doi: 10.3934/dcdsb.2018067 |
2020 Impact Factor: 1.392
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