Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two species nonlocal diffusion systems with free boundaries   We study a class of free boundary systems with nonlocal diffusion, which are
natural extensions of the corresponding free boundary problems of reaction
diffusion systems. As before the free boundary represents the spreading front
of the species, but here the population dispersal is described by "nonlocal
diffusion" instead of "local diffusion". We prove that such a nonlocal
diffusion problem with free boundary has a unique global solution, and for
models with Lotka-Volterra type competition or predator-prey growth terms, we
show that a spreading-vanishing dichotomy holds, and obtain criteria for
spreading and vanishing; moreover, for the weak competition case and for the
weak predation case, we can determine the long-time asymptotic limit of the
solution when spreading happens. Compared with the single species free boundary
model with nonlocal diffusion considered recently in \cite{CDLL}, and the two
species cases with local diffusion extensively studied in the literature, the
situation considered in this paper involves several extra difficulties, which
are overcome by the use of some new techniques.

33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga