Self-regulated biological transportation structures with general entropy dissipations, part Ⅰ: The 1D case

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-01-01 DOI:10.3934/jdg.2023022

Clarissa Astuto, Jan Haskovec, Peter Markowich, Simone Portaro

引用次数: 0

Abstract

We study self-regulating processes modeling biological transportation networks as presented in [15]. In particular, we focus on the 1D setting for Dirichlet and Neumann boundary conditions. We prove an existence and uniqueness result under the assumption of positivity of the diffusivity $ D $. We explore systematically various scenarios and gain insights into the behavior of $ D $ and its impact on the studied system. This involves analyzing the system with a signed measure distribution of sources and sinks. Finally, we perform several numerical tests in which the solution $ D $ touches zero, confirming the previous hints of local existence in particular cases.

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具有一般熵耗散的自我调节生物运输结构，部分Ⅰ:一维情况

我们研究了模拟生物运输网络的自调节过程，如[15]所示。我们特别关注Dirichlet和Neumann边界条件的一维设置。我们证明了在扩散系数为正的假设下的一个存在唯一性结果。我们系统地探索各种场景，并深入了解$ D $的行为及其对所研究系统的影响。这包括用源和汇的有符号测量分布来分析系统。最后，我们进行了几个解$ D $为零的数值测试，在特定情况下证实了前面的局部存在性提示。

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.