本项目旨在从研究一些经典的模型开始得到对非局部扩散和非局部反应的一般性认识和理论。参照经典微分方程理论的研究成果，我们将重点研究三个方面的科学问题。(1) MEMS模型：主要研究带有非局部项的MEMS模型的淬火(quench)现象，并以此为例侧重研究如何处理缺乏比较原理的非局部模型，特别是动态解收敛性的判别法则。(2) Gierer-Meinhardt模型及其影子系统：继续研究该模型全局解/爆破解的相关性质，同时以此为例研究反应扩散系统与它的影子系统之间的收敛关系。(3) 一般的带有非局部项的方程及影子系统：侧重稳定静态解的性态刻画。特别的，我们将分别考虑非局部扩散和非局部反应两种情况，并将探讨不同边值条件和区域的几何性质对稳定解性态的影响。

The purpose of this project is to promote the understanding of nonlocal diffusion and nonlocal reaction from more general level by studying several classical models first. Based on the development of theories of classical differential equations, we will carry on the investigation from three different aspects. (1) MEMS model: We will study quench phenomena in MEMS model with nonlocal terms and then use it as an example to further study how to handle nonlocal models where comparison principles fail. In particular, we aim to establish the criterion for the convergence of solutions in nonlocal models. (2) Gierer-Meinhardt model and its shadow system: First, we continue to study the properties of its global/blow-up solutions. Then we will investigate the convergence relations between reaction-diffusion systems and their shadow systems. (3) General nonlocal models and shadow systems: Mainly focus on the characterization of properties of stable steady states. In particular, during the studies of stable steady states, both nonlocal diffusion and nonlocal reaction will be considered respectively. Moreover, the effects of different types of boundary conditions and geometric properties of the domains will be investigated.