Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Large time behavior of a two phase extension of the porous medium
  equation   We study the large time behavior of the solutions to a two phase extension of
the porous medium equation, which models the so-called seawater intrusion
problem. The goal is to identify the self-similar solutions that correspond to
steady states of a rescaled version of the problem. We fully characterize the
unique steady states that are identified as minimizers of a convex energy and
shown to be radially symmetric. Moreover, we prove the convergence of the
solution to the time-dependent model towards the unique stationary state as
time goes to infinity. We finally provide numerical illustrations of the
stationary states and we exhibit numerical convergence rates.

5
The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin