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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

Yonggeun Cho 1, and  Tohru Ozawa 1,

1. 

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

Received  March 2006 Revised  October 2006 Published  January 2007

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 and Continuous Dynamical Systems, 2007, 17 (4) : 691-711. doi: 10.3934/dcds.2007.17.691
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