论文标题
反应扩散系统中波列的次谐波动力学
Subharmonic Dynamics of Wave Trains in Reaction Diffusion Systems
论文作者
论文摘要
我们研究了反应扩散系统中光谱稳定波列的稳定性和非线性局部动力学。对于\ mathbb {n} $中的每一个$ n \，这种$ t $ - 周期性的行进波很容易被认为是非线性渐近稳定（具有渐近阶段），当受指数的衰减速率呈$ nt $ nt $ - periodic时，即subharmonic，扰动。但是，允许的扰动尺寸和衰减的指数率都取决于$ n $，尤其是它们倾向于将零作为$ n \至\ infty $零，从而导致这种亚谐波稳定性结果缺乏均匀性。在这项工作中，我们基于作者的最新工作，并引入了一种方法，该方法使我们能够实现统一扰动的稳定性结果，该扰动在$ n $中是均匀的。当受到本地化的扰动（即可在线上的扰动）时，我们的工作是由此类波的动力学动机的，最近在许多作者那里受到了相当大的关注。
We investigate the stability and nonlinear local dynamics of spectrally stable wave trains in reaction-diffusion systems. For each $N\in\mathbb{N}$, such $T$-periodic traveling waves are easily seen to be nonlinearly asymptotically stable (with asymptotic phase) with exponential rates of decay when subject to $NT$-periodic, i.e., subharmonic, perturbations. However, both the allowable size of perturbations and the exponential rates of decay depend on $N$, and, in particular, they tend to zero as $N\to\infty$, leading to a lack of uniformity in such subharmonic stability results. In this work, we build on recent work by the authors and introduce a methodology that allows us to achieve a stability result for subharmonic perturbations which is uniform in $N$. Our work is motivated by the dynamics of such waves when subject to perturbations which are localized (i.e. integrable on the line), which has recently received considerable attention by many authors.
