A Domain Decomposition Method for Solution of a PDE-Constrained Generalized Nash Equilibrium Model of Biofilm Community Metabolism

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Applied Mathematics Pub Date : 2024-01-24 DOI:10.1137/22m1511023

Isaac Klapper, Daniel B. Szyld, Xinli Yu, Karsten Zengler, Tianyu Zhang, Cristal Zúñiga

引用次数: 0

Abstract

SIAM Journal on Applied Mathematics, Volume 84, Issue 1, Page 97-113, February 2024.
Abstract. Microbes are able to deploy different strategies in response to, and depending upon, local environmental conditions. In the setting of a microbial community, this property induces a Nash equilibrium problem because access to environmental resources is bounded. If microbes are also distributed in space, then those resources are subject to transport limitations (encoded in a PDE) and so microbial strategies at one location influence resources and, hence, microbial strategies, at another. Here we formulate the resulting PDE-coupled generalized Nash equilibrium problem for a multispecies biofilm community, and propose a domain-decomposition-based method for its solution. An example consisting of a model with two microbial species biofilm with 33 externally transported chemical concentrations is presented.

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用领域分解法求解生物膜群落代谢的 PDE 受限广义纳什均衡模型

SIAM 应用数学杂志》第 84 卷第 1 期第 97-113 页，2024 年 2 月。摘要微生物能够根据当地的环境条件部署不同的策略。在微生物群落的环境中，由于环境资源的获取是有限制的，因此这一特性导致了纳什均衡问题。如果微生物也分布在空间中，那么这些资源就会受到运输限制（用 PDE 编码），因此一个地点的微生物策略会影响另一个地点的资源，进而影响微生物策略。在这里，我们为一个多物种生物膜群落提出了由此产生的 PDE 耦合广义纳什均衡问题，并提出了一种基于领域分解的求解方法。我们将以两个微生物物种的生物膜模型为例，介绍 33 种外部传输的化学浓度。

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

SIAM Journal on Applied Mathematics 数学-应用数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

12 months

期刊介绍： SIAM Journal on Applied Mathematics (SIAP) is an interdisciplinary journal containing research articles that treat scientific problems using methods that are of mathematical interest. Appropriate subject areas include the physical, engineering, financial, and life sciences. Examples are problems in fluid mechanics, including reaction-diffusion problems, sedimentation, combustion, and transport theory; solid mechanics; elasticity; electromagnetic theory and optics; materials science; mathematical biology, including population dynamics, biomechanics, and physiology; linear and nonlinear wave propagation, including scattering theory and wave propagation in random media; inverse problems; nonlinear dynamics; and stochastic processes, including queueing theory. Mathematical techniques of interest include asymptotic methods, bifurcation theory, dynamical systems theory, complex network theory, computational methods, and probabilistic and statistical methods.