论文标题
周期性解决方案的存在和线性稳定性，用于自由边界问题，以周期性的外部营养供应肿瘤生长建模
The existence and linear stability of periodic solution for a free boundary problem modeling tumor growth with a periodic supply of external nutrients
论文作者
论文摘要
我们研究了一个自由边界问题，以T-周期性供应$φ（t）$的外部营养物质建模肿瘤生长。该模型包含两个参数$μ$和$ \widetildeσ$。我们首先证明（i）零径向对称解时且仅当$ \widetildeσ\ ge \ frac {1} {t} {t} \ int_ {0}^{t}φ（t}φ（t）d t t $ （ii）如果$ \wideTildeσ<\ frac {1} {t} \ int_ {0}^{t}^{t}φ（t）d t $，则存在一个唯一的径向对称的积极解决方案$ \ left（σ_{*}（r，t），p _ {p _ {p _ {*} $}（p _ { $ t $，它是所有$μ> 0 $的所有积极径向对称解决方案的全球吸引子。这些结果是Bai和Xu [pac的开放问题的完美答案。 J. Appl。数学。 2013（5），217-223]。然后，考虑非放射对称的扰动，我们证明存在一个常数的$μ_{\ ast}> 0 $ 0 $，使得$ \ weft（σ_{*}（r，t）（r，t），p _ {*}（r，t），r _ {*}（t），r _ {*}（t）\ right）对于$μ>μ_ {\ ast} $线性不稳定。
We study a free boundary problem modeling tumor growth with a T-periodic supply $Φ(t)$ of external nutrients. The model contains two parameters $μ$ and $\widetildeσ$. We first show that (i) zero radially symmetric solution is globally stable if and only if $\widetildeσ\ge \frac{1}{T} \int_{0}^{T} Φ(t) d t$; (ii) If $\widetildeσ<\frac{1}{T} \int_{0}^{T} Φ(t) d t$, then there exists a unique radially symmetric positive solution $\left(σ_{*}(r, t), p_{*}(r, t), R_{*}(t)\right)$ with period $T$ and it is a global attractor of all positive radially symmetric solutions for all $μ>0$. 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 $μ_{\ast}>0$ such that $\left(σ_{*}(r, t), p_{*}(r, t), R_{*}(t)\right)$ is linearly stable for $μ<μ_{\ast}$ and linearly unstable for $μ>μ_{\ast}$.
