关于移动域内细胞演化的非线性扩散模型

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Quarterly of Applied Mathematics Pub Date : 2024-05-21 DOI:10.1090/qam/1690

Tessa Thorsen, K. Trivisa

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引用次数: 0

摘要

我们研究了一个非线性模型的动力学，该模型描述了在多孔介质扩散和传输作用下以及在施用营养物和药物的情况下细胞的运动。速度场演变的动量方程受达西定律支配，而化学吸引剂（营养物或药物）的演变受扩散方程支配。系统在 R 3 \mathbb {R}^3 的移动域内演化，考虑到肿瘤的扩张或收缩。借助正则化近似方案和肿瘤运动的任意拉格朗日-欧勒（ALE）映射，确定了弱解的全局存在性。这项工作提供了一个既适合分析又适合模拟的变分框架。

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On a nonlinear diffussive model for the evolution of cells within a moving domain

We investigate the dynamics of a nonlinear model describing the motion of cells under the effect of porous-medium diffusion and transport and in the presence of nutrient and drug application. The momentum equation for the evolution of the velocity field is governed by Darcy’s law, while the evolution of the chemical attractant (nutrient or drug) is governed by a diffusion equation. The system evolves within a moving domain in R 3 \mathbb {R}^3 accounting for the expansion or shrinkage of the tumor. The global existence of weak solutions is established with the aid of a regularized approximating scheme and an Arbitrary Lagrangian-Eulerian (ALE) mapping for the motion of the tumor. This work provides a variational framework suitable for both analysis and simulations.

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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.