Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The existence and linear stability of periodic solution for a free
  boundary problem modeling tumor growth with a periodic supply of external
  nutrients   We study a free boundary problem modeling tumor growth with a T-periodic
supply $\Phi(t)$ of external nutrients. The model contains two parameters $\mu$
and $\widetilde{\sigma}$. We first show that (i) zero radially symmetric
solution is globally stable if and only if $\widetilde{\sigma}\ge \frac{1}{T}
\int_{0}^{T} \Phi(t) d t$; (ii) If $\widetilde{\sigma}<\frac{1}{T} \int_{0}^{T}
\Phi(t) d t$, then there exists a unique radially symmetric positive solution
$\left(\sigma_{*}(r, t), p_{*}(r, t), R_{*}(t)\right)$ with period $T$ and it
is a global attractor of all positive radially symmetric solutions for all
$\mu>0$. These results are a perfect answer to open problems in Bai and Xu
[Pac. J. Appl. Math. 2013(5), 217-223]. Then, considering non-radially
symmetric perturbations, we prove that there exists a constant $\mu_{\ast}>0$
such that $\left(\sigma_{*}(r, t), p_{*}(r, t), R_{*}(t)\right)$ is linearly
stable for $\mu<\mu_{\ast}$ and linearly unstable for $\mu>\mu_{\ast}$.

37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat