Electron. J. Diff. Equ.,
Vol. 2013 (2013), No. 44, pp. 127.
Wavebreaking phenomena and global solutions for
periodic twocomponent DullinGottwaldHolm systems
Min Zhu, Junxiang Xu
Abstract:
In this article we study the initialvalue problem for the periodic
twocomponent bfamily system, including a special case, when b = 2,
which is referred to as the twocomponent DullinGottwaldHolm (DGH) system.
We first show that the twocomponent bfamily system can be derived from the
theory of shallowwater waves moving over a linear shear flow. Then we
establish several results of blowup solutions corresponding to only
wave breaking with certain initial profiles for the periodic twocomponent
DGH system. Moreover, we determine the exact blowup 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
twocomponent DGH system.
Submitted November 14, 2012. Published February 8, 2013.
Math Subject Classifications: 35B30, 35G25.
Key Words: Twocomponent DullinGottwaldHolm system;
periodic twocomponent bfamily system; blowup;
wavebreaking; global solution.
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Min Zhu
Department of Mathematics,
Nanjing Forestry University
Nanjing 210037, China
email: zhumin@njfu.edu.cn


Junxiang Xu
Department of Mathematics,
Southeast University
Nanjing 211189, China
email: xujun@seu.edu.cn

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