Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the role of the range of dispersal in a nonlocal Fisher-KPP equation:
  an asymptotic analysis   In this paper, we study the asymptotic behavior as $\varepsilon\to0^+$ of
solutions $u\_\varepsilon$ to the nonlocal stationary Fisher-KPP type
equation$$
\frac{1}{\varepsilon^m}\int\_{\mathbb{R}^N}J\_\varepsilon(x-y)(u\_\varepsilon(y)-u\_\varepsilon(x))\mathrm{d}y+u\_\varepsilon(x)(a(x)-u\_\varepsilon(x))=0\text{
in }\mathbb{R}^N, $$where $\varepsilon>0$ and $0\leq m<2$. Under rather mild
assumptions and using very little technology, we prove that there exists one
and only one positive solution $u\_\varepsilon$ and that $u\_\varepsilon\to
a^+$ as $\varepsilon\to0^+$ where $a^+=\max\{0,a\}$. This generalizes the
previously known results and answers an open question raised by Berestycki,
Coville and Vo. Our method of proof is also of independent interest as it shows
how to reduce this nonlocal problem to a local one. The sharpness of our
assumptions is also briefly discussed.

35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph