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Global existence and blow-up phenomena for a weakly dissipative Degasperis-Procesi equation
On the Hunter--Saxton system
1. | Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan |
[1] |
Xiuting Li, Lei Zhang. The Cauchy problem and blow-up phenomena for a new integrable two-component peakon system with cubic nonlinearities. Discrete and Continuous Dynamical Systems, 2017, 37 (6) : 3301-3325. doi: 10.3934/dcds.2017140 |
[2] |
Joachim Escher, Olaf Lechtenfeld, Zhaoyang Yin. Well-posedness and blow-up phenomena for the 2-component Camassa-Holm equation. Discrete and Continuous Dynamical Systems, 2007, 19 (3) : 493-513. doi: 10.3934/dcds.2007.19.493 |
[3] |
Jingqun Wang, Lixin Tian, Weiwei Guo. Global exact controllability and asympotic stabilization of the periodic two-component $\mu\rho$-Hunter-Saxton system. Discrete and Continuous Dynamical Systems - S, 2016, 9 (6) : 2129-2148. doi: 10.3934/dcdss.2016088 |
[4] |
Shouming Zhou, Chunlai Mu, Liangchen Wang. Well-posedness, blow-up phenomena and global existence for the generalized $b$-equation with higher-order nonlinearities and weak dissipation. Discrete and Continuous Dynamical Systems, 2014, 34 (2) : 843-867. doi: 10.3934/dcds.2014.34.843 |
[5] |
Vural Bayrak, Emil Novruzov, Ibrahim Ozkol. Local-in-space blow-up criteria for two-component nonlinear dispersive wave system. Discrete and Continuous Dynamical Systems, 2019, 39 (10) : 6023-6037. doi: 10.3934/dcds.2019263 |
[6] |
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 |
[7] |
Xi Tu, Zhaoyang Yin. Local well-posedness and blow-up phenomena for a generalized Camassa-Holm equation with peakon solutions. Discrete and Continuous Dynamical Systems, 2016, 36 (5) : 2781-2801. doi: 10.3934/dcds.2016.36.2781 |
[8] |
Lei Zhang, Bin Liu. Well-posedness, blow-up criteria and gevrey regularity for a rotation-two-component camassa-holm system. Discrete and Continuous Dynamical Systems, 2018, 38 (5) : 2655-2685. doi: 10.3934/dcds.2018112 |
[9] |
Alejandro Sarria. Global estimates and blow-up criteria for the generalized Hunter-Saxton system. Discrete and Continuous Dynamical Systems - B, 2015, 20 (2) : 641-673. doi: 10.3934/dcdsb.2015.20.641 |
[10] |
Ying Fu, Changzheng Qu, Yichen Ma. Well-posedness and blow-up phenomena for the interacting system of the Camassa-Holm and Degasperis-Procesi equations. Discrete and Continuous Dynamical Systems, 2010, 27 (3) : 1025-1035. doi: 10.3934/dcds.2010.27.1025 |
[11] |
Yongsheng Mi, Boling Guo, Chunlai Mu. Well-posedness and blow-up scenario for a new integrable four-component system with peakon solutions. Discrete and Continuous Dynamical Systems, 2016, 36 (4) : 2171-2191. doi: 10.3934/dcds.2016.36.2171 |
[12] |
Min Li, Zhaoyang Yin. Blow-up phenomena and travelling wave solutions to the periodic integrable dispersive Hunter-Saxton equation. Discrete and Continuous Dynamical Systems, 2017, 37 (12) : 6471-6485. doi: 10.3934/dcds.2017280 |
[13] |
Jibin Li. Bifurcations and exact travelling wave solutions of the generalized two-component Hunter-Saxton system. Discrete and Continuous Dynamical Systems - B, 2014, 19 (6) : 1719-1729. doi: 10.3934/dcdsb.2014.19.1719 |
[14] |
Zhaoyang Yin. Well-posedness and blow-up phenomena for the periodic generalized Camassa-Holm equation. Communications on Pure and Applied Analysis, 2004, 3 (3) : 501-508. doi: 10.3934/cpaa.2004.3.501 |
[15] |
Jinlu Li, Zhaoyang Yin. Well-posedness and blow-up phenomena for a generalized Camassa-Holm equation. Discrete and Continuous Dynamical Systems, 2016, 36 (10) : 5493-5508. doi: 10.3934/dcds.2016042 |
[16] |
Kai Yan, Zhaoyang Yin. Well-posedness for a modified two-component Camassa-Holm system in critical spaces. Discrete and Continuous Dynamical Systems, 2013, 33 (4) : 1699-1712. doi: 10.3934/dcds.2013.33.1699 |
[17] |
Xinwei Yu, Zhichun Zhai. On the Lagrangian averaged Euler equations: local well-posedness and blow-up criterion. Communications on Pure and Applied Analysis, 2012, 11 (5) : 1809-1823. doi: 10.3934/cpaa.2012.11.1809 |
[18] |
Wenjing Zhao. Local well-posedness and blow-up criteria of magneto-viscoelastic flows. Discrete and Continuous Dynamical Systems, 2018, 38 (9) : 4637-4655. doi: 10.3934/dcds.2018203 |
[19] |
Luigi Forcella, Kazumasa Fujiwara, Vladimir Georgiev, Tohru Ozawa. Local well-posedness and blow-up for the half Ginzburg-Landau-Kuramoto equation with rough coefficients and potential. Discrete and Continuous Dynamical Systems, 2019, 39 (5) : 2661-2678. doi: 10.3934/dcds.2019111 |
[20] |
Tarek Saanouni. A note on global well-posedness and blow-up of some semilinear evolution equations. Evolution Equations and Control Theory, 2015, 4 (3) : 355-372. doi: 10.3934/eect.2015.4.355 |
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