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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:503

Article

Fernandez-Romero, A.¹  Guillen-Gonzalez, F.¹  Suarez, A.¹ 

[1] Univ Seville, Fac Matemat, Dept Ecuac Diferenc & Anal Numer, Seville, Spain

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

DOI  :  10.1016/j.jmaa.2021.125325

来源: Elsevier

【 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.

【 授权许可】

Free