Remarks on modified improved Boussinesq equations in one space dimension
Preprint Series # 723 Cho, Yonggeun and Ozawa, Tohru Remarks on modified improved Boussinesq equations in one space dimension. (2005); AbstractWe 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. Item Type:  Preprint 

Additional Information:  20 

Uncontrolled Keywords:  IMBq equation, small amplitude solution, global existence, scattering 

Subjects:  35xx PARTIAL DIFFERENTIAL EQUATIONS 

ID Code:  969 

