Population Dynamics in Hostile Neighborhoods

一个具有非局部扩散的Stefan型自由边界问题

A free boundary problem of Stefan type with nonlocal diffusion

我们介绍和分析一个非本地版本的单相Stefan问题，其中，在经典模型中，液相的体积的增长率是成比例的能量损失通过相间的速率。我们证明了存在性和唯一性的问题上提出的线上，和半线上的常数Dirichlet数据，并在径向的情况下，在几个维度。我们还描述了解及其自由边界的渐近行为。该模型可能是感兴趣的，以描述在恶劣的环境中的人口的蔓延。

对数扩散方程由混合分数阶算子的叠加所支配

Logistic diffusion equations governed by the superposition of operators of mixed fractional order

本文研究了由混合分数阶算子叠加驱动的对数扩散方程，在敌对环境中探讨种群生存与灭绝的条件及机制。

Dynamics of A Single Population Model with Memory Effect and Spatial Heterogeneity

In this paper, a single population model with memory effect and the heterogeneity of the environment, equipped with the Neumann boundary, is considered. The global existence of a spatial nonhomogeneous steady state is proved by the method of upper and lower solutions, which is asymptotically stable for relatively small memorized diffusion. However, after the memorized diffusion rate exceeding a critical value, spatial inhomogeneous periodic solution can be generated through Hopf bifurcation, if the integral of intrinsic growth rate over the domain is negative. Such phenomenon will never happen…

Novel Spatial Profiles of Population Distribution of Two Diffusive SIS Epidemic Models with Mass Action Infection Mechanism and Small Movement Rate for the Infected Individuals

In this paper, we are concerned with two SIS epidemic reaction-diffusion models with mass action infection mechanism of the form $SI$, and study the spatial profile of population distribution as the movement rate of the infected individuals is restricted to be small. For the model with a constant total population number, our results show that the susceptible population always converges to a positive constant which is indeed the minimum of the associated risk function, and the infected population either concentrates at the isolated highest-risk points or aggregates only on the highest-risk inte…