Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: How do degenerate mobilities determine singularity formation in
  Cahn-Hilliard equations?   Cahn-Hilliard models are central for describing the evolution of interfaces
in phase separation processes and free boundary problems. In general, they have
non-constant and often degenerate mobilities. However, in the latter case, the
spontaneous appearance of points of vanishing mobility and their impact on the
solution are not well understood. In this paper we develop a singular
perturbation theory to identify a range of degeneracies for which the solution
of the Cahn-Hilliard equation forms a singularity in infinite time. This
analysis forms the basis for a rigorous sharp interface theory and enables the
systematic development of robust numerical methods for this family of model
equations.

17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga