Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Numerical Investigation of a Dipole Type Solution for Unsteady
  Groundwater Flow with Capillary Retention and Forced Drainage   A model of unsteady filtration (seepage) in a porous medium with capillary
retention is considered. It leads to a free boundary problem for a generalized
porous medium equation where the location of the boundary of the water mound is
determined as part of the solution. The numerical solution of the free boundary
problem is shown to possess self-similar intermediate asymptotics. On the other
hand, the asymptotic solution can be obtained from a non-linear boundary value
problem. Numerical solution of the resulting eigenvalue problem agrees with the
solution of the partial differential equation for intermediate times. In the
second part of the work, we consider the problem of control of the water mound
extension by a forced drainage.

9
The categories of this paper are: nlin
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph