Dynamic bifurcation of the <Emphasis Type="Italic">n</Emphasis>-dimensional complex Swift-Hohenberg equation

This paper is concerned with the bifurcation of a complex Swift-Hohenberg equation. The attractor bifurcation of the complex Swift-Hohenberg equation on a one- dimensional domain （0, L） is investigated. It is shown that the n-dimensional complex Swift-Hohenberg equation bifurcates from the trivial solution to an attractor under the Dirichlet boundary condition on a general domain and under a periodic boundary condition when the bifurcation parameter crosses some critical values. The stability property of the bifurcation attractor is analyzed.     

一类旋转磁对流系统振幅方程的双波前解的存在性和稳定性分析

研究了旋转磁对流系统的振幅方程的一类稳态解的存在性和稳定性问题,得出了振幅方程的双波前解的存在性定理及相容性条件,通过变分特征化方法证明了方程解的不稳定性.     

n维复Swift-Hohenberg方程的动态分叉

考虑复Swift-Hohenberg方程的分叉问题．首先对复Swift-Hohenberg方程在一维区域(0,L)上的吸引子分叉进行了考虑．而后给出了n维复Swift-Hohenberg方程,在一般区域上Dirichlet边界条件下和周期边界条件下,当参数λ穿过某些分叉点时从平凡解处分叉出吸引子,并对吸引子分叉的稳定性进行了分析．