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# Remarks on modified improved Boussinesq equations in one space dimension

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 Please use this identifier to cite or link to this item:http://doi.org/10.14943/83873

 Title: Remarks on modified improved Boussinesq equations in one space dimension Authors: Cho, Yonggeun Browse this author Ozawa, Tohru Browse this author Keywords: IMBq equation small amplitude solution global existence scattering Issue Date: 2005 Journal Title: Hokkaido University Preprint Series in Mathematics Volume: 723 Start Page: 1 End Page: 15 Abstract: 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. Type: bulletin (article) URI: http://hdl.handle.net/2115/69531 Appears in Collections: 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

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