Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A generalized porous medium equation related to some singular
  quasilinear problems   In this paper we study existence and nonexistence of solutions for a
Dirichlet boundary value problem whose model is $$ \begin{cases}
-\sum_{m=1}^{\infty} a_m \Delta u^m= f&\text{in}\ \Omega \newline u=0 &
\text{on}\ \partial\Omega\,, \end{cases} $$ where $\Omega$ is a bounded domain
of $\mathbb{R}^N$, $a_m$ is a sequence of nonnegative real numbers, and $f$ is
in $L^q(\Omega)$, $q>\frac{N}{2}$.

3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph