Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A diffused interface with the advection term in a Sobolev space   We study the asymptotic limit of diffused surface energy in the van der
Waals--Cahn--Hillard theory when an advection term is added and the energy is
uniformly bounded. We prove that the limit interface is an integral varifold
and the generalized mean curvature vector is determined by the advection term.
As the application, a prescribed mean curvature problem is solved using the
min-max method.

29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int