Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A multiphase Cahn-Hilliard-Darcy model for tumour growth with necrosis   We derive a Cahn-Hilliard-Darcy model to describe multiphase tumour growth
taking interactions with multiple chemical species into account as well as the
simultaneous occurrence of proliferating, quiescent and necrotic regions. Via a
coupling of the Cahn-Hilliard-Darcy equations to a system of reaction-diffusion
equations a multitude of phenomena such as nutrient diffusion and consumption,
angiogenesis, hypoxia, blood vessel growth, and inhibition by toxic agents,
which are released for example by the necrotic cells, can be included. A new
feature of the modelling approach is that a volume-averaged velocity is used,
which dramatically simplifies the resulting equations. With the help of
formally matched asymptotic analysis we develop new sharp interface models.
Finite element numerical computations are performed and in particular the
effects of necrosis on tumour growth is investigated numerically.

8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int