当Allee阈值是一种进化特征时：持久性与灭绝
When the Allee threshold is an evolutionary trait: persistence vs. extinction
摘要：
我们考虑一个非局部的抛物型方程，它描述了由空间位置和表型性状构成的种群的动态，服从离散、突变和增长。增长项可以是Fisher-KPP型的，但也可能受到Allee效应的影响，该效应可以是弱的（非KPP单稳态非线性，可能退化）或强的（非线性）。生长的类型取决于变量$θ$的值：Allee阈值，在这里被认为是一种进化特征。在证明了Cauchy问题的适定性之后，我们研究了其解的长时间行为。由于模型的丰富性和各种现象之间的相互作用以及增长项的非局部性，结果（灭绝与持久性）是多种多样的，并与现有文献中关于局部反应扩散方程的早期结果形成鲜明对比。
英文摘要：
We consider a nonlocal parabolic equation describing the dynamics of a population structured by a spatial position and a phenotypic trait, submitted to dispersion , mutations and growth. The growth term may be of the Fisher-KPP type but may also be subject to an Allee effect which can be weak (non-KPP monostable nonlinearity, possibly degenerate) or strong (bistable nonlinearity). The type of growth depends on the value of a variable $θ$ : the Allee threshold, which is considered here as an evolutionary trait. After proving the well-posedness of the Cauchy problem, we study the long time behavior of the solutions. Due to the richness of the model and the interplay between the various phenomena and the nonlocality of the growth term, the outcomes (extinction vs. persistence) are various and in sharp contrast with earlier results of the existing literature on local reaction-diffusion equations.
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