论文标题
分析具有血管生成的非线性自由性肿瘤模型以及非生物和坏死相之间的联系
Analysis of a nonlinear free-boundary tumor model with angiogenesis and a connection between the nonnecrotic and necrotic phases
论文作者
论文摘要
本文涉及一个非线性游离边界问题，该问题模拟了具有罗宾边界条件的血管生成的球形对称肿瘤的生长。其中考虑了非核酸性肿瘤和坏死肿瘤。研究了解决方案的适当性和渐近行为。结果表明，存在两个阈值，由$ \tildeσ$和$σ^*$表示，在周围的营养浓度$ \barσ$上。如果$ \barσ\ leq \tildeσ$，那么被考虑的问题承认没有固定溶液，所有进化肿瘤最终都会消失，而如果$ \barσ> \tildeσ$，则承认一个独特的固定溶液，所有进化肿瘤都会融合到该休眠性肿瘤；此外，如果$ \tildeσ<\barσ\leqσ^*$和坏死，则休眠的肿瘤是无丝状的。还给出了非核酸和坏死阶段之间的连接和相互转变。
This paper is concerned with a nonlinear free boundary problem modeling the growth of spherically symmetric tumors with angiogenesis, set with a Robin boundary condition. In which, both nonnecrotic tumors and necrotic tumors are taken into consideration. The well-posedness and asymptotic behavior of solutions are studied. It is shown that there exist two thresholds, denoted by $\tildeσ$ and $σ^*$, on the surrounding nutrient concentration $\barσ$. If $\barσ\leq\tildeσ$, then the considered problem admits no stationary solution and all evolutionary tumors will finally vanish, while if $\barσ>\tildeσ$, then it admits a unique stationary solution and all evolutionary tumors will converge to this dormant tumor; moreover, the dormant tumor is nonnecrotic if $\tildeσ<\barσ\leqσ^*$ and necrotic if $\barσ>σ^*$. The connection and mutual transition between the nonnecrotic and necrotic phases are also given.
