On a Class of Nonlocal Continuity Equations on Graphs
Analysis of PDEs
2023-06-06 v1
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.
Cite
@article{arxiv.2209.15552,
title = {On a Class of Nonlocal Continuity Equations on Graphs},
author = {A. Esposito and F. S. Patacchini and A. Schlichting},
journal= {arXiv preprint arXiv:2209.15552},
year = {2023}
}