Diffusive Stability of Spatially Periodic Solutions of the Brusselator Model

Diffusive Stability of Spatially Periodic Solutions of the Brusselator Model
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Brusselator模型空间周期解的扩散稳定性

DOI：
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发表时间：
2016
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通讯作者：
R. Venkatraman
R. Venkatraman
中科院分区：
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文献类型：
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作者：
A. Sukhtayev;K. Zumbrun;Soyeun Jung;R. Venkatraman

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应用Mielke和Schneider在分析四阶标量Swift-Hohenberg方程时引入的Lyapunov-Schmidt约化方法，对由扩散子模型给出的正则二阶反应扩散方程组进行了严格的小振幅图灵斑图稳定性分析.我们的研究结果证实，稳定性是准确的预测在小振幅限制的正式Ginzburg-Landau振幅方程，严格验证了标准的弱不稳定近似和Eckhaus标准。
Applying the Lyapunov–Schmidt reduction approach introduced by Mielke and Schneider in their analysis of the fourth-order scalar Swift–Hohenberg equation, we carry out a rigorous small-amplitude stability analysis of Turing patterns for the canonical second-order system of reaction–diffusion equations given by the Brusselator model. Our results confirm that stability is accurately predicted in the small-amplitude limit by the formal Ginzburg–Landau amplitude equations, rigorously validating the standard weakly unstable approximation and the Eckhaus criterion.