Reaction–subdiffusion systems and memory: spectra, Turing instability and decay estimates
Reaction–subdiffusion systems and memory: spectra, Turing instability and decay estimates
复制标题
反应-亚扩散系统和记忆：光谱、图灵不稳定性和衰变估计
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
J. Rademacher
中科院分区：
文献类型：
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作者：
Jichen Yang;J. Rademacher
线性和非线性反应-亚扩散过程的建模比普通扩散过程更加精细，并引起不同的现象。所得到的方程通过时间分数导数具有具有时间记忆项的空间拉普拉斯函数。我们知道，精确的形式取决于扩散和反应的相互作用，并导致质的差异。我们通过色散关系定义广义谱来改进这些结果，这使我们能够检查不稳定性的开始，特别是检查图灵型不稳定性。对这些结果进行了数值说明。此外，我们还证明了一类亚扩散反应方程的稳定谱具有代数衰减，而另一类反应方程的稳定谱具有指数衰减。
The modelling of linear and nonlinear reaction-subdiffusion processes is more subtle than normal diffusion and causes different phenomena. The resulting equations feature a spatial Laplacian with a temporal memory term through a time fractional derivative. It is known that the precise form depends on the interaction of dispersal and reaction, and leads to qualitative differences. We refine these results by defining generalised spectra through dispersion relations, which allows us to examine the onset of instability and in particular inspect Turing type instabilities. These results are numerically illustrated. Moreover, we prove expansions that imply for one class of subdiffusion reaction equations algebraic decay for stable spectrum, whereas for another class this is exponential.