On the incompressible limit for a tumour growth model incorporating convective effects

IF 3.1 1区数学 Q1 MATHEMATICS

Communications on Pure and Applied Mathematics Pub Date : 2023-10-16 DOI:10.1002/cpa.22178

Noemi David, Markus Schmidtchen

引用次数: 0

Abstract

In this work we study a tissue growth model with applications to tumour growth. The model is based on that of Perthame, Quirós, and Vázquez proposed in 2014 but incorporates the advective effects caused, for instance, by the presence of nutrients, oxygen, or, possibly, as a result of self-propulsion. The main result of this work is the incompressible limit of this model which builds a bridge between the density-based model and a geometry free-boundary problem by passing to a singular limit in the pressure law. The limiting objects are then proven to be unique.

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考虑对流效应的肿瘤生长模型的不可压缩极限

在这项工作中，我们研究了一种应用于肿瘤生长的组织生长模型。该模型基于Perthame、Quirós和Vázquez在2014年提出的模型，但考虑了平流效应，例如营养物质、氧气的存在，或者可能是自推进的结果。这项工作的主要结果是该模型的不可压缩极限，它通过传递到压力定律中的奇异极限，在基于密度的模型和无几何边界问题之间架起了一座桥梁。然后证明限制对象是唯一的。

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

Communications on Pure and Applied Mathematics 数学-数学

CiteScore

6.70

自引率

3.30%

发文量

审稿时长

>12 weeks

期刊介绍： Communications on Pure and Applied Mathematics (ISSN 0010-3640) is published monthly, one volume per year, by John Wiley & Sons, Inc. © 2019. The journal primarily publishes papers originating at or solicited by the Courant Institute of Mathematical Sciences. It features recent developments in applied mathematics, mathematical physics, and mathematical analysis. The topics include partial differential equations, computer science, and applied mathematics. CPAM is devoted to mathematical contributions to the sciences; both theoretical and applied papers, of original or expository type, are included.