标题： 具有非局部扩散和自由边界的可约合作系统的长期行为 显示英文标题

标题： Longtime behaviors of a reducible cooperative system with nonlocal diffusions and free boundaries

摘要： 本文旨在理解具有非局部扩散和不同自由边界的可约合作系统的长期行为，该系统描述了两个互惠物种之间的相互作用。与不可约单稳态合作系统相比，我们关注的系统具有许多非负稳态，从而导致许多不同且丰富的长期行为。此外，由于半空间中可能出现的非负稳态非常量，我们需要进行更详细的分析来理解相应的稳态问题，这反过来又有助于我们对问题的长期行为进行完整的分类。本文还讨论了自由边界的扩散速度以及$(u,v)$在$t\to\infty$时的更精确极限，并指出如果核函数违反某些阈值条件，则可能发生加速扩散。 显示英文摘要

摘要： This paper aims at understanding the longtime behaviors of a reducible cooperative system with nonlocal diffusions and different free boundaries, describing the interactions of two mutually beneficial species. Compared with the irreducible and monostable cooperative system, the system we care about here has many nonnegative steady states, leading to much different and rich longtime behaviors. Moreover, since the possible nonnegative steady states on half space are non-constant, we need to employ more detailed analysis to understand the corresponding steady state problems which in turn helps us to derive a complete classification for the longtime behaviors of our problem. The spreading speeds of free boundaries and more accurate limits of $(u,v)$ as $t\to\infty$ are also discussed, and accelerated spreading can happen if some threshold conditions are violated by kernel functions.