Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Existence of Strong Solutions to the Cahn-Hilliard-Darcy system
  with mass source   We study a diffuse interface model describing the evolution of the flow of a
binary fluid in a Hele-Shaw cell. The model consists of a Cahn-Hilliard-Darcy
(CHD) type system with transport and mass source. A relevant physical
application is related to tumor growth dynamics, which in particular justifies
the occurrence of a mass inflow. We study the initial-boundary value problem
for this model and prove global existence and uniqueness of strong solutions in
two space dimensions as well as local existence in three space dimensions.

23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph