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

Abstract

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.

28 pages, 5 figures

References in corpus (2)

• Theoretical analysis for a PDE-ODE system related to a Glioblastoma tumor with vasculature
• Determining parameters giving different growths of a new Glioblastoma differential model

Cited by in corpus (4)

• An unconditionally energy stable and positive upwind DG scheme for the Keller-Segel model
• A Glioblastoma PDE-ODE model including chemotaxis and vasculature
• Hybrid PDE-ODE Models for Efficient Simulation of Infection Spread in Epidemiology
• Determining parameters giving different growths of a new Glioblastoma differential model