Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 44, pp. 1-27.

Title: Wave-breaking phenomena and global solutions for
       periodic two-component Dullin-Gottwald-Holm systems
        
Authors: Min Zhu (Nanjing Forestry Univ. , China)
         Junxiang Xu (Southeast Univ., Nanjing, China)

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.

Submitted November 14, 2012. Published February 08, 2013.
Math Subject Classifications: 35B30, 35G25.
Key Words: Two-component Dullin-Gottwald-Holm system; 
           periodic two-component b-family system;  blow-up;
           wave-breaking; global solution.