On small amplitude solutions to the generalized Boussinesq equations

Yonggeun Cho; Tohru Ozawa

doi:10.3934/dcds.2007.17.691

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2007, Volume 17, Issue 4: 691-711. Doi: 10.3934/dcds.2007.17.691

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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

Received: February 28, 2006

Revised: September 30, 2006

Published: September 2007

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Abstract

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 $\mathbb{R}^n, n \ge 1$.

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Mathematics Subject Classification: Primary: 35Q53; Secondary: 47J35.

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