双重特征值附近分支解的稳定性

Stability of Bifurcated Solutions Near a Double Eigenvalue

本文使用讨论稳定性的投影方法及标尺度技术研究了非线性分歧问题于其双重特征值附近各分支解的稳定性,证明了每个分支解的稳定性是由一个二阶矩阵的特征值决定的,并将所得结果应用于Cahn-Hillard-Schlgl反应-扩散方程。

The projection method and rescaling skills are used to deal with stability of bifurcated solutions near a double eigenvalue. Our conclusion is that the stability of each branch of solution is determined by the eigenvalues of a 2×2 matrix. Finally, the results are applied to CahnHilliard-Schlgl reaction-diffusion equations.