Published: On a class of nonlocal continuity equations on graphs

18 May 2023

The article with Antonio Esposito and Francesco S. Patacchini on a class of nonlocal continuity equations on graphs got published in the European Journal of Applied Mathematics. This is a follow-up work on our previous work also with Dejan Slepcev, where we introduced evolutions on graphs based on Upwind interpolation. In this work, we look at more general interpolation functions and provide a well-posedness theory based on a fixed point argument. Motivated by applications in data science, we study partial differential equations on graphs.