论文标题
分析具有非局部边界条件的肿瘤生长模型
Analysis of a tumor growth model with a nonlocal boundary condition
论文作者
论文摘要
在本文中，我们对使用治疗的肿瘤生长模型进行了彻底的数学分析。该模型是描述转移性肿瘤的演变和原发性肿瘤中存在的细胞数量的系统。以前的进化是通过线性传输方程来描述的，而后者则通过gompertzian型的普通微分方程来描述。这两个动力学通过非局部边界条件耦合，该条件考虑了肿瘤定植率。我们证明了一个存在结果，其中主要困难是处理耦合并考虑到治疗条款产生的时间不连续性的时间。我们还提出了突出不同处理作用的数值测试。
In this paper, we conduct a thorough mathematical analysis of a tumor growth model with treatments. The model is a system describing the evolution of metastatic tumors and the number of cells present in a primary tumor. The former evolution is described by a linear transport equation and the latter by an ordinary differential equation of Gompertzian type. The two dynamics are coupled through a nonlocal boundary condition that takes into account the tumor colonization rate. We prove an existence result where the main difficulty is to deal with the coupling and to take into account the time discontinuities generated by treatment terms. We also present numerical tests that highlight the effect of different treatments.
