Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Stefan problem for the Fisher-KPP equation with unbounded initial
  range   We consider the nonlinear Stefan problem $$
  \left \{ \begin{array} {ll}
  -d \Delta u=a u-b u^2 \;\; & \mbox{for } x \in \Omega (t), \; t>0,
  \\ u=0 \mbox{ and } u_t=\mu|\nabla_x u |^2 \;\;&\mbox{for } x \in
\partial\Omega (t), \; t>0, \\ u(0,x)=u_0 (x) \;\; & \mbox{for } x \in
\Omega_0, \end{array}\right. $$
  where $\Omega(0)=\Omega_0$ is an unbounded smooth domain in $\mathbb R^N$,
$u_0>0$ in $\Omega_0$ and $u_0$ vanishes on $\partial\Omega_0$. When $\Omega_0$
is bounded, the long-time behavior of this problem has been rather
well-understood by \cite{DG1,DG2,DLZ, DMW}. Here we reveal some interesting
different behavior for certain unbounded $\Omega_0$. We also give a unified
approach for a weak solution theory to this kind of free boundary problems with
bounded or unbounded $\Omega_0$.

32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int