Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharp Interface Limits of the Cahn-Hilliard Equation with Degenerate
  Mobility   In this work, the sharp interface limit of the degenerate Cahn-Hilliard
equation (in two space dimensions) with a polynomial double well free energy
and a quadratic mobility is derived via a matched asymptotic analysis involving
exponentially large and small terms and multiple inner layers. In contrast to
some results found in the literature, our analysis reveals that the interface
motion is driven by a combination of surface diffusion flux proportional to the
surface Laplacian of the interface curvature and an additional contribution
from nonlinear, porous-medium type bulk diffusion, For higher degenerate
mobilities, bulk diffusion is subdominant. The sharp interface models are
corroborated by comparing relaxation rates of perturbations to a radially
symmetric stationary state with those obtained by the phase field model.

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The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph