一类Boussinesq方程初值问题整体解的渐近性

Asymptotic Behavior of the Global Solution for a Generalized Boussinesq Equation with Initial Value

运用Fourier技巧,研究了一类Boussinesq方程初值问题,在一个Sobolev空间中得到了整体解的适定性,同时运用摄动方法得到了形式渐近解的合理性.

Using Fourier techniques, this paper deals with a Boussinesq equation with initial value, and the well-posedness of the global solution is gained. The validity of the formal asymptotic solution is established in a suitable Sobolev space by the perturbation method.