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arXiv · 2209.15552

On a Class of Nonlocal Continuity Equations on Graphs

A. Esposito·F. S. Patacchini·A. Schlichting
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Abstract

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.

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A. Esposito, F. S. Patacchini, A. Schlichting. 2022-09-30. On a Class of Nonlocal Continuity Equations on Graphs. https://doi.org/10.1017/s0956792523000128

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