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 Electronic Journal of Differential Equations , 2013, Abstract: In this article we study the initial-value problem for the periodic two-component b-family system, including a special case, when b = 2, which is referred to as the two-component Dullin-Gottwald-Holm (DGH) system. We first show that the two-component b-family system can be derived from the theory of shallow-water waves moving over a linear shear flow. Then we establish several results of blow-up solutions corresponding to only wave breaking with certain initial profiles for the periodic two-component DGH system. Moreover, we determine the exact blow-up rate and lower bound of the lifespan for the system. Finally, we give a sufficient condition for the existence of the strong global solution to the periodic two-component DGH system.
 Duc-Trung Hoang Mathematics , 2014, Abstract: We investigate wave breaking for the Dullin-Gottwald-Holm equation and the two-component Dullin-Gottwald-Holm system. We establish a new blow-up criterion for the general case $\gamma+c_0\alpha^2 \geq 0$ involving local-in-space conditions on the initial data.
 江苏科技大学学报(自然科学版) , 2006, Abstract: ？研究了一类由dullin,gottwald和holm提出的新的含线性和非线性色散项的完全可积型浅水波方程(称为dullin-gottwald-holm方程)的反散射问题。首先利用反散射方法建立了dgh方程的反散射方程以及一系列求解方程,并且给出了解的一般形式,然后利用散射数据以参数形式给出了dgh方程的1-孤子解,最后画出了几个取特殊值时解的侧面图。
 江苏科技大学学报(自然科学版) , 2010, Abstract: ？研究了一类新型非线性浅水波方程(dullin-gottwald-holm方程,简称为dgh方程)的散射逼近问题,文章首先通过对与离散谱相对应的特征函数的归一化变形,给出了dgh方程的散射数据;其次利用dgh方程的lax对和liouville变换求出了初始位势函数,最终论证了dgh方程的可积性.
 Xinglong Wu Mathematics , 2014, Abstract: The present paper is mainly concerned with the blow-up phenomena and exponential decay of solution for a three-component Camassa-Holm equation. Comparing with the result of Hu, ect. in the paper[1], a new wave-breaking solution is obtained. The results of exponential decay of solution in our paper cover and extent the corresponding results in [12, 19, 22].
 Mathematics , 2015, Abstract: In this paper we mainly study the Cauchy problem for a generalized Camassa-Holm equation. First, by using the Littlewood-Paley decomposition and transport equations theory, we establish the local well-posedness for the Cauchy problem of the equation in Besov spaces. Then we give a simply blow-up criterion for the Cauchy problem of the equation. we present a blow-up result and the exact blow-up rate of strong solutions to the equation by making use of the conservation law and the obtained blow-up criterion.Finally, we verify that the system possesses peakon solutions.
 Mathematics , 2015, Abstract: This paper is devoted to an integrable two-component Camassa-Holm system with cubic nonlinearity, which includes the cubic Camassa-Holm equation (also called the Fokas-Olver-Rosenau-Qiao equation) as a special case. The one peaked solitons (peakons) and two peakon solutions are described in an explicit formula. Then, the local well-posedness for the Cauchy problem of the system is studied. Moreover, we target at the precise blow-up scenario for strong solutions to the system, and establish a new blow-up result with respect to the initial data.
 Mathematics , 2011, Abstract: We first establish local well-posedness for a periodic 2-component Camassa-Holm equation with vorticity. We then present a global existence result for strong solutions to the equation. We finally obtain several blow-up results and the blow-up rate of strong solutions to the equation.
 作者,朱师师,臧林恩 - , 2017, Abstract: 本文研究了具零阶耗散的双成分Camassa-Holm方程的Cauchy问题.由Kato定理得到局部适定性的结果，然后研究了解的整体存在性和爆破现象.In this paper, we study the two-component Camassa-Holm equation with the zero order dissipation. By using the Kato's theorem, the local well-posedness is obtain. Then we study the global existence and blow-up phenomena of the solutions for the Cauchy problem
 Physics , 2014, Abstract: This paper is concerned with a multi-component Camassa-Holm system, which has been proven to be integrable and has peakon solutions. This system includes many one-component and two-component Camassa-Holm type systems as special cases. In this paper, we first establish the local well-posedness and a continuation criterion for the system, then we present several global existence or blow-up results for two important integrable two-component subsystems. Our obtained results cover and improve recent results in \cite{Gui,yan}.
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