Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergence of solutions for the fractional Cahn-Hilliard system   This paper deals with the Cauchy-Dirichlet problem for the fractional
Cahn-Hilliard equation. The main results consist of global (in time) existence
of weak solutions, characterization of parabolic smoothing effects (implying
under proper condition eventual boundedness of trajectories), and convergence
of each solution to a (single) equilibrium. In particular, to prove the
convergence result, a variant of the so-called \L ojasiewicz-Simon inequality
is provided for the fractional Dirichlet Laplacian and (possibly) non-analytic
(but $C^1$) nonlinearities.

7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc