## 抄録

We study the existence and scattering of global small amplitude solutions to modified improved Boussinesq equations in one dimension with nonlinear term f(u) behaving as a power u^{p} as u → 0. Solutions are considered in H^{s} space for all s> 1/2. 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 s = 3/2 for sufficiently small Cauchy data. In this paper, we prove that p can be reduced to be greater than 9/2 at s> 17/10 and the corresponding solution u has the time decay, such as ∥u(t)∥_{L∞} = O(t^{-2/5}) as t → ∞. We also prove non-existence of non-trivial asymptotically free solutions for 1 < p ≤ 2 under vanishing condition near zero frequency on asymptotic states.

本文言語 | English |
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ページ（範囲） | 1949-1963 |

ページ数 | 15 |

ジャーナル | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |

巻 | 462 |

号 | 2071 |

DOI | |

出版ステータス | Published - 2006 |

外部発表 | はい |

## ASJC Scopus subject areas

- 数学 (全般)
- 工学（全般）
- 物理学および天文学（全般）