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

In this work we analyse a PDE-ODE problem modelling the evolution of Glioblastoma, which includes an anisotropic nonlinear diffusion term with velocity increasing respect to vasculature. First, prove existence global in time weak-strong solutions using regularization technique via artificial ODE-system and fixed point argument. addition, stability results critical points are given under some constraints on parameters. Finally, design fully discrete finite element scheme for model preserves pointwise energy estimates continuous problem.