Solving a chemotaxis-haptotaxis system in 2D using Generalized Finite Difference Method

被引：16
|
作者：
Benito, J. J. [1 ]
Garcia, A. [1 ]
Gavete, L. [2 ]
Negreanu, M. [3 ]
Urena, F. [1 ]
Vargas, A. M. [3 ]
机构：
[1] UNED, ETSII, Madrid, Spain
[2] UPM, ETSIM, Madrid, Spain
[3] UCM, Dept Anal Matemat & Matemat Aplicada, Madrid, Spain
来源：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2020年 / 80卷 / 05期
关键词：
Chemotaxis-haptotaxis; Generalized Finite Differences; Meshless method; CLASSICAL-SOLUTIONS; GLOBAL EXISTENCE; EQUATIONS; INVASION; TISSUE; MODEL;
D O I：
10.1016/j.camwa.2020.05.008
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study a mathematical model of cancer cell invasion of tissue (extracellular matrix) consisting of a system of reaction-diffusion-taxis partial differential equations which describes the interactions between cancer cells, the matrix degrading enzyme and the host tissue. We analyze the local stability of the constant equilibrium solutions to the chemotaxis-haptotaxis system, we derive a discretization of the system by means of the Generalized Finite Difference Method (GFDM) and we prove the convergence of the discrete solution to the analytical one. Also, we provide several numerical examples on the applications of this meshless method over regular and irregular domains. (C) 2020 Elsevier Ltd. All rights reserved.
引用
收藏
页码：762 / 777
页数：16
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