Remarks on modified improved Boussinesq equations in one space dimension
Remarks on modified improved Boussinesq equations in one space dimension
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DOI：
10.1098/rspa.2006.1675
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发表时间：
2006-07
期刊：
影响因子：
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通讯作者：
Yonggeun Cho;T. Ozawa
中科院分区：
文献类型：
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作者：
Yonggeun Cho;T. Ozawa
研究了一维以非线性项为幂函数的修正改进的Boussinesq方程整体小振幅解的存在性和散射性。在太空中，所有人都在考虑解决方案。根据S的取值，确定了功率非线性指数p。刘(刘1996，印第安纳大学数学课。J.45,797-816)对于足够小的柯西数据，得到了大于8的最小值p。本文证明了p可以约化为大于At，并且相应的解u具有时间衰减性，如As。我们还证明了在零频率附近渐近状态下非平凡渐近自由解的不存在性。
We study the existence and scattering of global small amplitude solutions to modified improved Boussinesq equations in one dimension with nonlinear term behaving as a power as . Solutions are considered in space for all . According to the value of s, the power nonlinearity exponent p is determined. Liu (Liu 1996 Indiana Univ. Math. J. 45, 797–816) obtained the minimum value of p greater than 8 at for sufficiently small Cauchy data. In this paper, we prove that p can be reduced to be greater than at and the corresponding solution u has the time decay, such as as . We also prove non-existence of non-trivial asymptotically free solutions for under vanishing condition near zero frequency on asymptotic states.