Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Travelling wave solutions for gravity fingering in porous media flows   We study an imbibition problem for porous media. When a wetted layer is above
a dry medium, gravity leads to the propagation of the water downwards into the
medium. In experiments, the occurrence of fingers was observed, a phenomenon
that can be described with models that include hysteresis. In the present
paper, we describe a single finger in a moving frame and set up a free boundary
problem to describe the shape and the motion of one finger that propagates with
a constant speed. We show the existence of solutions to the travelling wave
problem and investigate the system numerically.

3
The categories of this paper are: physics
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga