图上的非局部交叉作用系统：非二次Finslerian结构和非线性迁移率
Nonlocal cross-interaction systems on graphs: Nonquadratic Finslerian structure and nonlinear mobilities
摘要：
研究了具有非线性迁移和非局部相互作用的两种群系统在图上的演化，图的顶点由任意的正测度给出。为此，我们扩展了最近推出的$2$ -Wasserstein型拟度量的广义图，这是基于迎风插值，两种系统的情况下，凹，非线性迁移率，和$p\ne 2$。我们提供了一个严格的解释的相互作用系统作为梯度流的芬斯勒设置，所产生的新的准度量。
英文摘要：
We study the evolution of a system of two species with nonlinear mobility and nonlocal interactions on a graph whose vertices are given by an arbitrary, positive measure. To this end, we extend a recently introduced $2$-Wasserstein-type quasi-metric on generalized graphs, which is based on an upwind-interpolation, to the case of two-species systems, concave, nonlinear mobilities, and $p\ne 2$. We provide a rigorous interpretation of the interaction system as a gradient flow in the Finslerian setting, arising from the new quasi-metric.
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