论文标题
在图形上的一类非局部连续性方程上
On a Class of Nonlocal Continuity Equations on Graphs
论文作者
论文摘要
在数据科学中的应用中，我们研究了图形的部分微分方程。通过经典的固定点参数，我们显示了对图上一类非局部连续性方程的解决方案的存在和独特性。我们考虑一般的插值函数，这些函数产生了各种不同的动力学，例如来自溶液依赖性速度场的非本地相互作用动力学。我们的分析揭示了与更标准的欧几里得空间的结构差异，因为某些类似特性依赖于所选的插值。
Motivated by applications in data science, we study partial differential equations on graphs. By a classical fixed-point argument, we show existence and uniqueness of solutions to a class of nonlocal continuity equations on graphs. We consider general interpolation functions, which give rise to a variety of different dynamics, e.g., the nonlocal interaction dynamics coming from a solution-dependent velocity field. Our analysis reveals structural differences with the more standard Euclidean space, as some analogous properties rely on the interpolation chosen.
