Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the parabolicity of the Muskat problem: Well-posedness, fingering,
  and stability results   We consider in this paper the Muskat problem in a periodic geometry and
incorporate capillary as well as gravity effects in the modelling. The problem
re-writes as an abstract evolution equation and we use this property to prove
well-posedness of the problem and to establish exponential stability of some
flat equilibrium. Using bifurcation theory we also find finger shaped
steady-states which are all unstable.

3
The categories of this paper are: physics
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
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The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg