标题： 非局部相互作用方程的图到局部极限 显示英文标题

标题： Graph-to-local limit for the nonlocal interaction equation

摘要： 我们研究一类具有张量迁移率的非局部偏微分方程，在空间中，这些方程是通过从定位无限图上的非局部动力学渐近得到的。 我们的策略依赖于两种方程的变分结构，分别是黎曼和芬斯勒梯度流。 更准确地说，我们证明了图上的非局部相互作用方程的弱解在欧几里得空间中收敛到上述具有张量迁移率的非局部相互作用方程的弱解。 这突显了图的一个有趣特性，即作为所研究方程的潜在空间离散化。 显示英文摘要

摘要： We study a class of nonlocal partial differential equations presenting a tensor-mobility, in space, obtained asymptotically from nonlocal dynamics on localising infinite graphs. Our strategy relies on the variational structure of both equations, being a Riemannian and Finslerian gradient flow, respectively. More precisely, we prove that weak solutions of the nonlocal interaction equation on graphs converge to weak solutions of the aforementioned class of nonlocal interaction equation with a tensor-mobility in the Euclidean space. This highlights an interesting property of the graph, being a potential space-discretisation for the equation under study.