论文标题
在断开域中的一类非本地Fisher-KPP方程的稳态的性质
Properties of steady states for a class of non-local Fisher-KPP equations in disconnected domains
论文作者
论文摘要
这里研究的问题是，在域外，在域外的域中，涉及分数laplacian（ - $δ$）^$α$的Fisher-KPP方程的非平凡界限稳态的存在和独特性。更具体地说，我们在一般碎片的无界领域的情况下研究了此类问题。实际上，我们利用非本地分散剂来在稳态上提供分析界（仅取决于域）。这些结果与生物学有关。例如，我们的结果提供了关于碎片区域中非本地扩散的物种生存的域标准。这些标准主要涉及运算符（ - $δ$）^$α$的第一个特征值的符号 - 在域外有差异条件的域中ID。为此，我们在一维情况下两个紧凑型贴片之间的距离表现出了该主要特征值的连续性。最后结果的主要新颖性是距离0的连续性。
The question studied here is the existence and uniqueness of a non-trivial bounded steady state of a Fisher-KPP equation involving a fractional Laplacian (--$Δ$)^$α$ in a domain with Dirichlet conditions outside of the domain. More specifically, we investigate such questions in the case of general fragmented unbounded domains. Indeed, we take advantage of the non-local dispersion in order to provide analytic bounds (which depend only on the domain) on the steady states. Such results are relevant in biology. For instance, our results provide criteria on the domain for the subsistence of a species subject to a non-local diffusion in a fragmented area. These criteria primarily involve the sign of the first eigenvalue of the operator (--$Δ$)^$α$ -- Id in a domain with Dirichlet conditions outside of the domain. To this end, we exhibit a result of continuity of this principal eigenvalue with respect to the distance between two compact patchs in the one dimensional case. The main novelty of this last result is the continuity up to the distance 0.
