Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On uniqueness of large solutions of nonlinear parabolic equations in
  nonsmooth domains   We study the existence and uniqueness of the positive solutions of the
problem (P): $\partial_tu-\Delta u+u^q=0$ ($q>1$) in $\Omega\times (0,\infty)$,
$u=\infty$ on $\partial\Omega\times (0,\infty)$ and $u(.,0)\in L^1(\Omega)$,
when $\Omega$ is a bounded domain in $\mathbb R^N$. We construct a maximal
solution, prove that this maximal solution is a large solution whenever
$q<N/(N-2)$ and it is unique if $\partial\Omega=\partial\bar\Omega^c$. If
$\partial\Omega$ has the local graph property, we prove that there exists at
most one solution to problem (P)

36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat