Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global existence and asymptotic behavior of solutions to a nonlocal
  Fisher-KPP type problem   In this work, we consider a nonlocal Fisher-KPP reaction-diffusion problem
with Neumann boundary condition and nonnegative initial data in a bounded
domain in $\mathbb{R}^n (n \ge 1)$, with reaction term $u^\alpha(1-m(t))$,
where $m(t)$ is the total mass at time $t$. When $\alpha \ge 1$ and the initial
mass is greater than or equal to one, the problem has a unique nonnegative
classical solution. While if the initial mass is less than one, then the
problem admits a unique global solution for $n=1,2$ with any $1 \le \alpha <2$
or $n \ge 3$ with any $1 \le \alpha < 1+2/n$. Moreover, the asymptotic
convergence to the solution of the heat equation is proved. Finally, some
numerical simulations in dimensions $n=1,2$ are exhibited. Especially, for
$\alpha>2$ and the initial mass is less than one, our numerical results show
that the solution exists globally in time and the mass tends to one as time
goes to infinity.

11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn