Remarks on modified improved Boussinesq equations in one space dimension

• Cho Yonggeun

• Ozawa Tohru

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 $u \to 0$. Solutions in $H^s$ space are considered for all $s > 0$. According to the value of $s$, the power nonlinearity exponent $p$ is determined. Liu \cite{liu} obtained the minimum value of $p$ greater than $8$ at $s = \frac32$ for sufficiently small Cauchy data. In this paper, we prove that $p$ can be reduced to be greater than $\frac92$ at $s > \frac85$ and the corresponding solution $u$ has the time decay such as $\|u( t)\|_{L^\infty} = O(t^{-\frac25})$ as $t \to \infty$. We also prove nonexistence of nontrivial asymptotically free solutions for $1 < p \le 2$ under vanishing condition near zero frequency on asymptotic states.

収録刊行物

• Hokkaido University Preprint Series in Mathematics

  Hokkaido University Preprint Series in Mathematics 723 1-15, 2005

  Department of Mathematics, Hokkaido University

キーワード

• IMBq equation
• small amplitude solution
• global existence
• scattering

詳細情報

• CRID: 1390853649725441664
• NII論文ID: 120006459431
• DOI: 10.14943/83873
• HANDLE: 2115/69531
• 本文言語コード: en
• データソース種別:
  • JaLC
  • IRDB
  • CiNii Articles
• 抄録ライセンスフラグ: 使用可