Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mathematical Analysis of Nonlocal PDEs for Network Generation   In this paper, we study a certain class of nonlocal partial differential
equations (PDEs). The equations arise from a key problem in network science,
i.e., network generation from local interaction rules, which result in a change
of the degree distribution as time progresses. The evolution of the generating
function of this degree distribution can be described by a nonlocal PDE. To
address this equation we will rigorously convert it into a local first order
PDE. Then, we use theory of characteristics to prove solvability and regularity
of the solution. Next, we investigate the existence of steady states of the
PDE. We show that this problem reduces to an implicit ODE, which we
subsequently analyze. Finally, we perform numerical simulations, which show
stability of the steady states.

29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org