Department of Mathematics, Nanjing Forestry University
Nanjing 210037, China
email: zhumin@njfu.edu.cn
Department of Mathematics, Southeast University
Nanjing 211189, China
email: xujun@seu.edu.cn
Min Zhu, Junxiang Xu
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 8, 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.
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Min Zhu Department of Mathematics, Nanjing Forestry University Nanjing 210037, China email: zhumin@njfu.edu.cn |
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| Junxiang Xu Department of Mathematics, Southeast University Nanjing 211189, China email: xujun@seu.edu.cn |
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