一类具有Dirichlet边界条件的振幅方程的稳定性与分岔研究（英文）

Stability and Bifurcation Analysis of an Amplitude Equation with Dirichlet Boundary Conditions

本文研究一个偏微分方程组的平凡稳态解(0,0)的稳定性和分岔的问题,所研究的方程组是一个定义在有界区域(0,L)上有着Dirichlet边界条件的振幅方程.文中区间长度L被看成是一个分岔参数.文章考虑平凡稳态解(0,0)处的渐近行为,利用扰动理论的方法,获得非平凡解分岔结果,进一步地分析了非平凡分岔解的稳定性及其渐近行为.

This paper focuses on the bifurcation and stability of the trivial solution （0,0） of a particular system of parabolic partial differential equations. The equation is as an amplitude equation on a bounded domain （0, L） with Dirichlet boundary conditions. In this paper, the asymptotic behavior of the stationary solution （0,0） of the amplitude equation is considered. With the length L of the domain considered as bifurcation parameter, branches of nontrivial solutions are shown by the perturbation method. Besides, in this paper, a study is made on local behavior of these branches. Moreover, the stability of the bifurcated solutions are analyzed as well.