论文标题
当Allee阈值是进化特征时：持久性与灭绝
When the Allee threshold is an evolutionary trait: persistence vs. extinction
论文作者
论文摘要
我们考虑了一个非局部抛物线方程，描述了由空间位置和表型性状构成的人群的动力学，并提交给分散，突变和生长。生长项可能是Fisher-KPP类型的，但也可能受到弱效应（非kpp单稳定的非线性，可能是退化）或强（可bistable bistable demearity）。增长的类型取决于变量$θ$的值：Allee阈值，在这里被视为进化特征。在证明了库奇问题的适当性之后，我们研究了解决方案的长时间行为。由于模型的丰富性以及各种现象与生长术语的非局部性之间的相互作用，结果（灭绝与持久性）是各种各样的，并且与现有有关局部反应扩散方程的文献的早期结果形成了鲜明的对比。
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.
