Instability of planar interfaces in reaction-diffusion systems
Instability of planar interfaces in reaction-diffusion systems
复制标题
反应扩散系统中平面界面的不稳定性
DOI：
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发表时间：
1994
期刊：
影响因子：
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通讯作者：
Y. Nishiura
中科院分区：
文献类型：
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作者：
M. Taniguchi;Y. Nishiura
研究了二维反应扩散方程组平面前沿解的不稳定性。让$vareps $表示接口的宽度。当界面沿着切向的长度超过$O（vareps ^{{1 /2}}）$时，平面前缘解（或内部过渡层为平面的解）失去稳定性。最快增长的波长为O（varepa ^{{1 /3}}）$，这是系统固有的，由非线性系数和扩散系数决定。这些量的完全渐近特征为$vareps 通过分析从线性本征值问题导出的所谓奇异色散关系，给出了。数值计算也证实了理论上预测的最快增长的波浪图案实际上是由随机扰动的平面前引起的。
Instability of planar front solutions to reaction-diffusion systems in two space dimensions is studied. Let $varepsilon $ denote the width of interface. Then the planar front solution—or a solution having an internal transition layer which is flat—loses its stability when the length of interface along the tangential direction exceeds $O(varepsilon ^{{1 /2}} )$. The wavelength of the fastest growth is of $O(varepsilon ^{{1 /3}} )$ which is inherent in the system and determined by the nonlinearity and diffusion coefficients. Complete asymptotic characterization of these quantities as $varepsilon o 0$ is given by the analysis of what is called the singular dispersion relation derived from the linearized eigenvalue problem. The numerical computations also confirm that the theoretically predicted fastest growth wavy pattern actually arises from a randomly perturbed planar front.