In this paper we consider the propagation speed in a reaction diffusion system with an anomalous Lvy process diffusion, modeled by a nonlocal equation with a fractional Laplacian and a generalized monostable or ignition nonlinearity. Given a typical Heaviside initial datum, we show that the speed of interface propagation displays an algebraic rate behavior in time, in contrast to the known linear rate in the classical model of Brownian motion and the exponential rate in the KPP model with the anomalous diffusion, and depends on the sensitive balance between the anomaly of the diffusion process and the strength of monostable reaction. In particular, for the combustion model with a fractional Laplacian (−Δ) ^s , we show that the speed of propagation transits continuously from being linear in time, when a traveling wave solution exists for s ∈ (1/2, 1), to being algebraic in time with a power reciprocal to 2s, when no traveling wave solution exists for s ∈ (0, 1/2).

在本文中，我们考虑了具有异常 Lvy 过程扩散的反应扩散系统中的传播速度，该系统由具有分数拉普拉斯算子和广义单稳态或点火非线性的非局部方程建模。给定一个典型的 Heaviside 初始数据，我们表明界面传播速度随时间显示代数速率行为，与布朗运动经典模型中的已知线性速率和具有异常扩散的 KPP 模型中的指数速率形成对比，并且取决于扩散过程的异常与单稳态反应强度之间的敏感平衡。特别是，对于具有分数拉普拉斯算子 (−Δ) ^s的燃烧模型 ，我们表明，当s ∈ (1/2, 1)存在行波解时，传播速度从时间上的线性连续过渡到时间上的代数，其幂为 2 s 的倒数，当没有行波时s ∈ (0, 1/2)存在解。