论文标题
具有血管生成的自由边界肿瘤模型的渐近稳定性
Asymptotic stability for a free boundary tumor model with angiogenesis
论文作者
论文摘要
在本文中，我们研究了一个自由边界问题，该问题将脉管系统建模实体瘤生长建模，从而为肿瘤提供营养。这是罗宾边界条件的特征。它是最近建立的[离散续。 dyn。系统。 39（2019）2473-2510]，对于该模型，存在一个阈值$μ^\ ast $，因此在非radial扰动下以$ 0 <μ<μ<μ^\ ast $ untereartial稳定的唯一径向对称的固定解决方案是线性稳定的，对于$>μ>μ>μ^\ ast $ ust $。在本文中，我们进一步研究了径向对称的固定解的非线性稳定性，该解决方案引入了一个重要的数学难度：由于模式1术语的扰动，限制球的中心不知道。我们证明了一个新的固定点定理来解决此问题，最后获得径向对称的固定溶液在忽略翻译时以$ 0 <μ<μ^\ ast $而非线性稳定。
In this paper, we study a free boundary problem modeling solid tumor growth with vasculature which supplies nutrients to the tumor; this is characterized in the Robin boundary condition. It was recently established [Discrete Cont. Dyn. Syst. 39 (2019) 2473-2510] that for this model, there exists a threshold value $μ^\ast$ such that the unique radially symmetric stationary solution is linearly stable under non-radial perturbations for $0<μ<μ^\ast$ and linearly unstable for $μ>μ^\ast$. In this paper we further study the nonlinear stability of the radially symmetric stationary solution, which introduces a significant mathematical difficulty: the center of the limiting sphere is not known in advance owing to the perturbation of mode 1 terms. We prove a new fixed point theorem to solve this problem, and finally obtain that the radially symmetric stationary solution is nonlinearly stable for $0<μ<μ^\ast$ when neglecting translations.
