Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Parabolic power concavity and parabolic boundary value problems   This paper is concerned with power concavity properties of the solution to
the parabolic boundary value problem \begin{equation} \tag{$P$}
\left\{\begin{array}{ll} \partial_t u=\Delta u +f(x,t,u,\nabla u) &
\mbox{in}\quad\Omega\times(0,\infty),\vspace{3pt}\\ u(x,t)=0 &
\mbox{on}\quad\partial \Omega\times(0,\infty),\vspace{3pt}\\ u(x,0)=0 &
\mbox{in}\quad\Omega, \end{array} \right. \end{equation} where $\Omega$ is a
bounded convex domain in ${\bf R}^n$ and $f$ is a nonnegative continuous
function in $\Omega\times(0,\infty)\times{\bf R}\times{\bf R}^n$. We give a
sufficient condition for the solution of $(P)$ to be parabolically power
concave in $\bar{\Omega}\times[0,\infty)$.

30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th