Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The generalized porous medium equation on graphs: existence and
  uniqueness of solutions with $\ell^1$ data   We study solutions of the generalized porous medium equation on infinite
graphs. For nonnegative or nonpositive integrable data, we prove the existence
and uniqueness of mild solutions on any graph. For changing sign integrable
data, we show existence and uniqueness under extra assumptions such as local
finiteness or a uniform lower bound on the node measure.

32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph