论文标题
运输反应系统：高维域和定性二分法
Transport-Reaction Systems: Higher-Dimensional Domains and a Qualitative Dichotomy
论文作者
论文摘要
我们在任意尺寸的超立方体上研究通用线性传输反应系统，并具有周期性边界条件。运输反应系统通常用于模拟颗粒，细菌或动物的有限速度运动和相互作用。我们首先显示弱频谱映射定理，并演示其“应用”。其次，我们引入了一定类别的所谓双曲线不稳定性，这为一维域上的运输驱动不稳定性提供了自然的框架：它们是图灵模式，或者越来越多地振荡双曲线不稳定。作为副产品，获得了图灵模式存在的新代数条件。
We study general linear transport-reaction systems on an arbitrary dimensional hypercube with periodic boundary conditions. Transport-reaction systems are often used to model the finite speed movement and interaction of particles, bacteria or animals. We first show a weak spectral mapping theorem and demonstrate its' application. Secondly, we introduce a certain class of so-called hyperbolic instabilities, which provide a natural framework for transport-driven instabilities on one-dimensional domains: They are either Turing patterns or increasingly oscillating hyperbolic instabilities. A new algebraic condition for the existence of Turing patterns is obtained as a side-product.
