论文标题
反应扩散系统中的前部选择通过扩散正常形式
Front selection in reaction-diffusion systems via diffusive normal forms
论文作者
论文摘要
我们表明，如边缘稳定性的猜想所预测的那样，由反应扩散系统建模的入侵过程中的传播速度由边缘光谱稳定性条件确定。这个猜想最近在标量方程式中解决了。在这里，我们为多组件案例提供了完整的证明。主要的新难度在于精确地表征了入侵前沿中的扩散动态。为了克服这一点，我们引入了坐标转换，使我们能够识别仅依靠通用边缘稳定性假设的领先阶扩散方程。然后，我们能够使用自相似的变量来详细描述前沿中的扩散动力学，我们将其与唤醒中的行进入侵前锋匹配。然后，我们通过在非线性迭代方案中控制这些匹配误差来建立前选择，并依赖于对入侵前沿的线性化的尖锐估计。我们简要讨论了参数强制振幅方程，竞争性Lotka-Volterra系统和肿瘤生长模型的应用。
We show that propagation speeds in invasion processes modeled by reaction-diffusion systems are determined by marginal spectral stability conditions, as predicted by the marginal stability conjecture. This conjecture was recently settled in scalar equations; here we give a full proof for the multi-component case. The main new difficulty lies in precisely characterizing diffusive dynamics in the leading edge of invasion fronts. To overcome this, we introduce coordinate transformations which allow us to recognize a leading order diffusive equation relying only on an assumption of generic marginal pointwise stability. We are then able to use self-similar variables to give a detailed description of diffusive dynamics in the leading edge, which we match with a traveling invasion front in the wake. We then establish front selection by controlling these matching errors in a nonlinear iteration scheme, relying on sharp estimates on the linearization about the invasion front. We briefly discuss applications to parametrically forced amplitude equations, competitive Lotka-Volterra systems, and a tumor growth model.
