In this work we analyse a PDE-ODE problem modelling the evolution of a Glioblastoma, which includes chemotaxis term directed to vasculature. First, we obtain some a priori estimates for the (possible) solutions of the model. In particular, under some conditions on the parameters, we obtain that the system does not develop blow-up at finite time. In addition, we design a fully discrete finite element scheme for the model which preserves some pointwise estimates of the continuous problem. Later, we make an adimensional study in order to reduce the number of parameters. Finally, we detect the main parameters determining different width of the ring formed by proliferative and necrotic cells and different regular/irregular behaviour of the tumor surface.

翻译：在这项工作中,我们分析一个PDE-ODE问题模型,以模拟Glioblastoma的演变,其中包括针对血管的化毒学术语。首先,我们获得一些模型(可能的)解决办法的先验估计,特别是根据参数的某些条件,我们发现系统在有限的时间内不会产生爆炸。此外,我们为模型设计了一个完全独立的有限元素系统,保留对持续问题的某种点性估计。随后,我们进行一个维维学研究,以减少参数的数量。最后,我们检测出决定肿瘤表面的增生细胞和坏疽细胞以及不同正常/不正常行为所形成的环状不同宽度的主要参数。