论文标题
非局部扩散的非自主Fisher-KPP方程的扩散特性
Spreading properties for non-autonomous Fisher-KPP equations with nonlocal diffusion
论文作者
论文摘要
我们研究了由薄尾核驱动的非自主Fisher-KPP方程的溶液的渐近速度。在本文中，我们关注紧凑的支持和指数衰减的初始数据。对于一般时间的异质性，我们提供了解决方案扩散速度的较低和上层估计，该速度按时间的最小平均值表示，该时间的变化系数变化了。在对这些系数的一些更强的时间平均假设下，我们证明了这些解决方案以某种确定的速度传播。在此分析中，一个重要的困难来自于非局部扩散产生的溶液的正则化湖。通过精致的分析，我们为配备合适的初始数据的Logistic方程的某些解决方案得出了一些规律性估计（在很长一段时间内均匀的连续性类型）。然后，这些结果用于处理更通用的非线性，并得出相当普遍的扩散速度结果。
We investigate the asymptotic speed of spread of the solutions of a non-autonomous Fisher-KPP equation with nonlocal diffusion, driven by a thin-tailed kernel. In this paper, we are concerned with both compactly supported and exponentially decaying initial data. For general time heterogeneity, we provide lower and upper estimates of the spreading speed of the solutions, which is expressed in term of the least mean of the time varying coefficients of the problem. Under some stronger time averaging assumptions for these coefficients, we prove that these solutions propagate with some determined speed. In this analysis, an important difficulty comes from the lake of regularization for the solutions arising with nonlocal diffusion. Through delicate analysis we derive some regularity estimates (of uniform continuity type for the large time) for some solutions of the logistic equation equipped with suitable initial data. These results are then used to handle more general nonlinearities and derive a rather general spreading speed results.
