论文标题
与脉管系统取决于扩散的混合肿瘤模型的理论和数值分析
Theoretical and numerical analysis for a hybrid tumor model with diffusion depending on vasculature
论文作者
论文摘要
在这项工作中，我们分析了对胶质母细胞瘤的演变进行建模的PDE-ode问题，其中包括各向异性非线性扩散项，扩散速度相对于脉管系统而增加。首先，我们使用正则化技术通过人工扩散和固定点参数证明了全局弱 - 突变解决方案的存在。此外，临界点的稳定性结果是在某些参数的限制下给出的。最后，我们为模型设计了一个完全离散的有限元方案，该方案保留了连续问题的点和能量估计。
In this work we analyse a PDE-ODE problem modelling the evolution of a Glioblastoma, which includes an anisotropic nonlinear diffusion term with a diffusion velocity increasing with respect to vasculature. First, we prove the existence of global in time weak-strong solutions using a regularization technique via an artificial diffusion in the ODE-system and a fixed point argument. In addition, stability results of the critical points are given under some constraints on parameters. Finally, we design a fully discrete finite element scheme for the model which preserves the pointwise and energy estimates of the continuous problem.
