The Long Time Behavior of Solutions for a Generalized Boussinesq System

摘要

The initial-boundary value problem is investigated for a generalized Boussinesq equation with the quadratic nonlinearity. For small initial data and homogeneous boundary conditions, its solution is constructed in the form of a series which converges absolutely and uniformly. The long time asymp-totic expansion of the solution is acquired to show the nonlinear effects of amplitude.