Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The nonlocal-interaction equation near attracting manifolds   We study the approximation of the nonlocal-interaction equation restricted to
a compact manifold $\mathcal{M}$ embedded in $\mathbb{R}^d$, and more generally
compact sets with positive reach (i.e. prox-regular sets). We show that the
equation on $\mathcal{M}$ can be approximated by the classical
nonlocal-interaction equation on $\mathbb{R}^d$ by adding an external potential
which strongly attracts to $\mathcal{M}$. The proof relies on the
Sandier--Serfaty approach to the $\Gamma$-convergence of gradient flows. As a
by-product, we recover well-posedness for the nonlocal-interaction equation on
$\mathcal{M}$. Uniqueness, on the other hand, is established using a stability
argument. We also provide an another approximation to the interaction equation
on $\mathcal{M}$, based on iterating approximately solving an interaction
equation on $\mathbb{R}^d$ and projecting to $\mathcal{M}$. 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.

16
The categories of this paper are: stat
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys