论文标题
入侵残留不稳定：前动力学案例研究
Invasion into remnant instability: a case study of front dynamics
论文作者
论文摘要
我们研究了在特殊但通用的情况下，入侵过程表现出残余不稳定的侵害，通过一个传播的阵线来侵入不稳定的状态。在这里，残余不稳定性是指以下事实：在任何指数加权的空间中，在以线性入侵速度移动的框架中，空间恒定的入侵状态在任何指数加权的空间中是线性不稳定的。我们的主要结果是针对典型模型耦合时空振荡和单调动力学的典型模型耦合的非线性渐近稳定性。我们通过将扰动分解为两部分来建立稳定性：一个在加权空间中有界，第二个是在加权空间中无限的，但在未加权的空间中以指数级的速率均匀收敛至零。有趣的是，在某些情况下，长期数值模拟显示出明显的不稳定。我们展示了这种不稳定性是如何由圆形误差引起的，这些误差引入了其他非谐振线性模式的线性谐振耦合，并确定加速的入侵速度。
We study the invasion of an unstable state by a propagating front in a peculiar but generic situation where the invasion process exhibits a remnant instability. Here, remnant instability refers to the fact that the spatially constant invaded state is linearly unstable in any exponentially weighted space in a frame moving with the linear invasion speed. Our main result is the nonlinear asymptotic stability of the selected invasion front for a prototypical model coupling spatio-temporal oscillations and monotone dynamics. We establish stability through a decomposition of the perturbation into two pieces: one that is bounded in the weighted space and a second that is unbounded in the weighted space but which converges uniformly to zero in the unweighted space at an exponential rate. Interestingly, long-time numerical simulations reveal an apparent instability in some cases. We exhibit how this instability is caused by round-off errors that introduce linear resonant coupling of otherwise non-resonant linear modes, and we determine the accelerated invasion speed.
