A coupled Cahn–Hilliard model for the proliferative-to-invasive transition of hypoxic glioma cells

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Quarterly of Applied Mathematics Pub Date : 2020-09-15 DOI:10.1090/qam/1585

Lu Li, A. Miranville, R. Guillevin

引用次数: 4

Abstract

Our aim in this paper is to prove the existence of solutions for a model for the proliferative-to-invasive transition of hypoxic glioma cells. The equations consist of the coupling of a reaction-diffusion equation for the tumor density and of a Cahn–Hilliard type equation for the oxygen concentration. The main difficulty is to prove the existence of a biologically relevant solution. This is achieved by considering a modified equation and taking a logarithmic nonlinear term in the Cahn–Hilliard equation.

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缺氧胶质瘤细胞增殖到侵袭过渡的耦合Cahn-Hilliard模型

我们在这篇文章中的目的是为了证明缺氧胶质瘤细胞增殖到侵袭性转变模型的存在性。该方程由肿瘤密度的反应扩散方程和氧浓度的Cahn-Hilliard型方程的耦合组成。主要的困难是证明存在与生物学相关的解决方案。这是通过考虑一个修正方程和在Cahn-Hilliard方程中取一个对数非线性项来实现的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Quarterly of Applied Mathematics 数学-应用数学

CiteScore

1.90

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： The Quarterly of Applied Mathematics contains original papers in applied mathematics which have a close connection with applications. An author index appears in the last issue of each volume. This journal, published quarterly by Brown University with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website.