Papers › The nonlocal-interaction equation near attracting manifolds
The nonlocal-interaction equation near attracting manifolds
Francesco S. Patacchini, Dejan Slepčev
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
We study the approximation of the nonlocal-interaction equation restricted to a compact manifold ℳ embedded in ℝᵈ, and more generally compact sets with positive reach (i.e. prox-regular sets). We show that the equation on ℳ can be approximated by the classical nonlocal-interaction equation on ℝᵈ by adding an external potential which strongly attracts to ℳ. The proof relies on the Sandier--Serfaty approach to the Γ-convergence of gradient flows. As a by-product, we recover well-posedness for the nonlocal-interaction equation on ℳ. Uniqueness, on the other hand, is established using a stability argument. We also provide an another approximation to the interaction equation on ℳ, based on iterating approximately solving an interaction equation on ℝᵈ and projecting to ℳ. We show convergence of this scheme, together with an estimate on the rate of convergence. Finally, we conduct numerical experiments, for both the attractive-potential-based and the projection-based approaches, that highlight the effects of the geometry on the dynamics.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections