Theoretical and numerical analysis for a hybrid tumor model with diffusion depending on vasculature

[摘要] A B S T R A C T 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. (c) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-11-15

[关键词] Tumor model;Glioblastoma;PDE-ODE system;Numerical scheme