Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability Results on Radial Porous Media and Hele-Shaw Flows with
  Variable Viscosity Between Two Moving Interfaces   We perform a linear stability analysis of three-layer radial porous media and
Hele-Shaw flows with variable viscosity in the middle layer. A nonlinear change
of variables results in an eigenvalue problem that has time-dependent
coefficients and eigenvalue-dependent boundary conditions. We study this
eigenvalue problem and find upper bounds on the spectrum. We also give a
characterization of the eigenvalues and prescribe a measure for which the
eigenfunctions are complete in the corresponding $L^2$ space. The limit as the
viscous gradient goes to zero is compared with previous results on multi-layer
radial flows. We then numerically compute the eigenvalues and obtain, among
other results, optimal profiles within certain classes of functions.

24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys