Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Impact of Time Delay and Angiogenesis in a Tumor Model   We consider a free boundary tumor model under the presence of angiogenesis
and time delays in the process of proliferation, in which the cell location is
incorporated. It is assumed that the tumor attracts blood vessels at a rate
proportional to $\alpha$, and a parameter $\mu$ is proportional to the
`aggressiveness' of the tumor. In this paper, we first prove that there exists
a unique radially symmetric stationary solution $\left(\sigma_{*}, p_{*},
R_{*}\right)$ for all positive $\alpha$, $\mu$. Then a threshold value
$\mu_\ast$ is found such that the radially symmetric stationary solution is
linearly stable if $\mu<\mu_\ast$ and linearly unstable if $\mu>\mu_\ast$. Our
results indicate that the increase of the angiogenesis parameter $\alpha$ would
result in the reduction of the threshold value $\mu_\ast$; adding the time
delay would not alter the threshold value $\mu_\ast$, but result in a larger
stationary tumor, and the larger the tumor aggressiveness parameter $\mu$ is,
the greater impact of time delay would have on the size of the stationary
tumor.

1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat