本文研究带Direchlet边界条件的模型问题,利用多重尺度法和二次方法,在自由端的Barber条件,并通过边界层理论的渐近匹配技术进行了分析.反映了从线性稳定性研究到非线性系统的动态过程,得到了关于解的依赖性与短暂性的发展规律.%In this paper we first use a multiple scale or two-timing method to study this model with Dirichlet boundary condition. Then, we impose the known Barber condition at the free end. This system is analyzed by the asymptotic matching techniques of boundary layer theory to derive short-time, long-time and uniform expansions. Most importantly, all analysis is extended from the traditional linear stablity considerations into the nonlinear regime and dynamic information about the history dependence and temporal evolution of the solution is obtained.
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