Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Well-posedness and long-time behavior of a non-autonomous
  Cahn-Hilliard-Darcy system with mass source modeling tumor growth   In this paper, we study an initial boundary value problem of the
Cahn-Hilliard-Darcy system with a non-autonomous mass source term $S$ that
models tumor growth. We first prove the existence of global weak solutions as
well as the existence of unique local strong solutions in both 2D and 3D. Then
we investigate the qualitative behavior of solutions in details when the
spatial dimension is two. More precisely, we prove that the strong solution
exists globally and it defines a closed dynamical process. Then we establish
the existence of a minimal pullback attractor for translated bounded mass
source $S$. Finally, when $S$ is assumed to be asymptotically autonomous, we
demonstrate that any global weak/strong solution converges to a single steady
state as $t\to+\infty$. An estimate on the convergence rate is also given.

27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom