Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Synchronising and Non-synchronising Dynamics for a Two-species
  Aggregation Model   This paper deals with analysis and numerical simulations of a one-dimensional
two-species hyperbolic aggregation model. This model is formed by a system of
transport equations with nonlocal velocities, which describes the aggregate
dynamics of a two-species population in interaction appearing for instance in
bacterial chemotaxis. Blow-up of classical solutions occurs in finite time.
This raises the question to define measure-valued solutions for this system. To
this aim, we use the duality method developed for transport equations with
discontinuous velocity to prove the existence and uniqueness of measure-valued
solutions. The proof relies on a stability result. In addition, this approach
allows to study the hyperbolic limit of a kinetic chemotaxis model. Moreover,
we propose a finite volume numerical scheme whose convergence towards
measure-valued solutions is proved. It allows for numerical simulations
capturing the behaviour after blow up. Finally, numerical simulations
illustrate the complex dynamics of aggregates until the formation of a single
aggregate: after blow-up of classical solutions, aggregates of different
species are synchronising or nonsynchronising when collide, that is move
together or separately, depending on the parameters of the model and masses of
species involved.

23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio