Convergence rate for the incompressible limit of nonlinear diffusion–advection equations

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-08-02 DOI:10.4171/aihpc/53

Noemi David, Tomasz Dkebiec, B. Perthame

引用次数: 10

Abstract

The incompressible limit of nonlinear diffusion equations of porous medium type has attracted a lot of attention in recent years, due to its ability to link the weak formulation of cell-population models to free boundary problems of Hele-Shaw type. Although vast literature is available on this singular limit, little is known on the convergence rate of the solutions. In this work, we compute the convergence rate in a negative Sobolev norm and, upon interpolating with BV -uniform bounds, we deduce a convergence rate in appropriate Lebesgue spaces. 2010 Mathematics Subject Classification. 35K57; 35K65; 35Q92; 35B45;

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非线性扩散-平流方程不可压缩极限的收敛速率

多孔介质型非线性扩散方程的不可压缩极限由于能够将细胞种群模型的弱公式与Hele-Shaw型的自由边界问题联系起来，近年来引起了人们的广泛关注。尽管关于这个奇异极限有大量的文献，但关于解的收敛速度却知之甚少。在这项工作中，我们计算了负Sobolev范数下的收敛速度，并在用BV -一致界插值的基础上，我们推导了适当的Lebesgue空间中的收敛速度。2010数学学科分类。35K57;35 k65;35 q92;35 b45;

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.