Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uniform in Time Interacting Particle Approximations for Nonlinear
  Equations of Patlak-Keller-Segel type   We study a system of interacting diffusions that models chemotaxis of
biological cells or microorganisms (referred to as particles) in a chemical
field that is dynamically modified through the collective contributions from
the particles. Such systems of reinforced diffusions have been widely studied
and their hydrodynamic limits that are nonlinear non-local partial differential
equations are usually referred to as Patlak-Keller-Segel (PKS) equations. Under
the so-called "quasi-stationary hypothesis" on the chemical field the limit PDE
is closely related to granular media equations that have been extensively
studied probabilistically in recent years. Solutions of classical PKS solutions
may blow up in finite time and much of the PDE literature has been focused on
understanding this blow-up phenomenon. In this work we study a modified form of
the PKS equation for which global existence and uniqueness of solutions holds.
Our goal is to analyze the long-time behavior of the particle system
approximating the equation. We establish, under suitable conditions, uniform in
time convergence of the empirical measure of particle states to the solution of
the PDE. We also provide uniform in time exponential concentration bounds for
rate of the above convergence under additional integrability conditions.
Finally, we introduce an Euler discretization scheme for the simulation of the
interacting particle system and give error bounds that show that the scheme
converges uniformly in time and in the size of the particle system as the
discretization parameter approaches zero.

27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th