On small amplitude solutions to the generalized Boussinesq equations

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October 2007, 17(4): 691-711. doi: 10.3934/dcds.2007.17.691

On small amplitude solutions to the generalized Boussinesq equations

1.	Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan

Received March 2006 Revised October 2006 Published January 2007

Abstract
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We study the existence and scattering of global small amplitude solutions to generalized Boussinesq (Bq) and improved modified Boussinesq (imBq) equations with nonlinear term $f(u)$ behaving as a power $u^p$ as $u \to 0$ in $\mathbb{R}^n, n \ge 1$.

Keywords: global existence, generalized Bq and imBq equations, small amplitude solution, scattering..

Mathematics Subject Classification: Primary: 35Q53; Secondary: 47J3.

Citation: Yonggeun Cho, Tohru Ozawa. On small amplitude solutions to the generalized Boussinesq equations. Discrete & Continuous Dynamical Systems - A, 2007, 17 (4) : 691-711. doi: 10.3934/dcds.2007.17.691

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