Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonlinear boundary value problems relative to one dimensional heat
  equation   We consider the problem of existence of a solution $u$ to $\partial_t
u-\partial_{xx} u = 0$ in $(0,T)\times\mathbb{R}_+$ subject to the boundary
condition $-u_x(t,0)+g(u(t,0))=\mu$ on $(0,T)$ where $\mu$ is a measure on
$(0,T)$ and $g$ a continuous nondecreasing function. When $p>1$ we study the
set of self-similar solutions of $\partial_t u-\partial_{xx} u = 0$ in
$\mathbb{R}_+\times\mathbb{R}_+$ such that $-u_x(t,0)+u^p=0$ on $(0,\infty)$.
At end, we present various extensions to a higher dimensional framework.

31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg