Global existence and asymptotic behavior for a generalized Boussinesq
type equation without dissipation
Abstract
In this paper, we study the Cauchy problem for a generalized Boussinesq
type equation in $\mathbb{R}^n$. We establish a
dispersive estimate for the linear group associated with the generalized
Boussinesq type equation. As applications, the global existence, decay
and scattering of solutions are established for small initial data.