| Cahn-Hilliard-Schlgl反应-扩散方程分叉问题 |
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| 引用本文： | 屈乐伟,陆启韶.Cahn-Hilliard-Schlgl反应-扩散方程分叉问题[J].北京航空航天大学学报,1992(2). |
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| 作者姓名： | 屈乐伟 陆启韶 |
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| 作者单位： | 航空航天部质量司应用数理系
(屈乐伟)，航空航天部质量司应用数理系(陆启韶) |
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| 摘 要： | 本文利用Lyapunov-Schmidt约化方法、奇异性理论及摄动方法,对服从Cahn-Hilliard广义扩散定律的带有Schlgl反应项的Cahn-Hilliard-Schlgl反应-扩散方程的分叉情况进行了研究。研究结果表明,C-H-S方程可以产生单模态的空间周期一次和二次分叉。特别地,经小扰动的退化的C-H-S方程,在不同条件下,还可能产生不同形式的更为复杂的双模态混合的二次分叉。本文还给出了分叉类型和一次分叉解的近似表达式。
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| 关 键 词： | 分叉 摄动 奇异性 |
BIFURCATIONS OF CAHN-HILLIARD-SCHLOGL REACTION-DIFFUSION EQUATION |
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| Qu Lewei Lu Qishao.BIFURCATIONS OF CAHN-HILLIARD-SCHLOGL REACTION-DIFFUSION EQUATION[J].Journal of Beijing University of Aeronautics and Astronautics,1992(2). |
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| Authors: | Qu Lewei Lu Qishao |
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| Abstract: | Bifurcation of Cahn-Hilliard-Schlogl reaction diffusion equations,in which the reaction term is Schlogl's one and the diffusion term is governed by Cahn-Hilliard's generalized diffusion law,are studied by means of Lyapunov-Schmidt reduction method.singularity theory and perturbation method.It is shown that C-H-S equation have spatially periodic primary and secondary bifurcations with simple mode.Especially,the perturbed degenerate D-H-S equation,under different conditions,may have different kinds of double mixed-mode.The kinds of the bifurcations and ap-poraximate expressions of this primary bifurcations are given in the paper. |
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| Keywords: | bifurcation perturbation singularity |
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