Volume 56, Number 2, March-April 2022
|Page(s)||407 - 431|
|Published online||18 February 2022|
A Glioblastoma PDE-ODE model including chemotaxis and vasculature
Dpto. Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, Sevilla, Spain
* Corresponding author: firstname.lastname@example.org
Accepted: 26 January 2022
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.
Mathematics Subject Classification: 35A01 / 35B40 / 35M10 / 35Q92 / 47J35 / 92B05
Key words: Glioblastoma / chemotaxis / PDE-ODE system / numerical scheme
© The authors. Published by EDP Sciences, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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