Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal singularities of initial functions for solvability of a
  semilinear parabolic system   Let $(u,v)$ be a nonnegative solution to the semilinear parabolic system \[
\mbox{(P)} \qquad \cases{ \partial_t u=D_1\Delta u+v^p, & $x\in{\bf
R}^N,\,\,\,t>0,$\\ \partial_t v=D_2\Delta v+u^q, & $x\in{\bf R}^N,\,\,\,t>0,$\\
(u(\cdot,0),v(\cdot,0))=(\mu,\nu), & $x\in{\bf R}^N,$ } \] where $D_1$,
$D_2>0$, $0<p\le q$ with $pq>1$ and $(\mu,\nu)$ is a pair of nonnegative Radon
measures or nonnegative measurable functions in ${\bf R}^N$. In this paper we
study sufficient conditions on the initial data for the solvability of
problem~(P) and clarify optimal singularities of the initial functions for the
solvability.

16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph