%0 Journal Article
%T Wave-breaking phenomena and global solutions for periodic two-component Dullin-Gottwald-Holm systems
%A Min Zhu
%A Junxiang Xu
%J Electronic Journal of Differential Equations
%D 2013
%I Texas State University
%X 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.
%K Two-component Dullin-Gottwald-Holm system
%K periodic two-component b-family system
%K blow-up
%K wave-breaking
%K global solution
%U http://ejde.math.txstate.edu/Volumes/2013/44/abstr.html