有扩散不稳定性的四阶反应-扩散系统的空间周期结构

SPATIALLY PERIODIC STRUCTURES OF A FOURTH ORDER REACTION-DIFFUSION SYSTEM WITH DIFFUSION INSTABILITY

本文利用分叉理论研究一个含参数的有扩散不稳定性的四阶反应-扩散系统的空间周期结构问题,其中扩散项服从Cahn-Hillard广义扩散定律。首先通过稳定性和奇异性的分析得到从空间均匀定态产生空间周期定态的判别准则,然后利用奇异摄动方法获得这个空间周期定态的二阶近似解。本文的理论结果很好地符合文献[3]中的数值结果。

Spatially periodic structures of a parameterized fourth order reaction-diffusion system with-diffusion instability, where the diffusion term is governed by Cahn-Hillard's generalized diffusion law, are studied by means of bifurcation theory. A criterion of bifurcation for generating ipatially periodic steady states from spatially homogeneous steady states is provided through stability and singularity analysis. The second order approximation of spatially periodic steady states. is obtained by singular perturbation technique. The theoretical results in this paper are in good accord ance with numerical results in [3] .