Cross diffusion models in complex frameworks From microscopic to macroscopic

IF 3.6 1区 数学 Q1 MATHEMATICS, APPLIED
D. Burini, N. Chouhad
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引用次数: 0

Abstract

This paper deals with the micro-macro derivation of models from the underlying description provided by methods of the kinetic theory for active particles. We consider the so-called exotic models according to the definition proposed in in [9]. The first part of the presentation focuses on a survey and a critical analysis of some phenomenological models known in the literature. We refer to a selection of case studies, in detail: transport of virus models, social dynamics, and Keller-Segel in a fluid. The second part shows how an Hilbert type approach can be developed to derive models at the macroscale from the underlying description provided by the kinetic theory of active particles. The third part deals with the derivation of macroscopic models corresponding to the selected case studies. Finally, a forward look into the future research perspectives is proposed.
复杂框架中的交叉扩散模型——从微观到宏观
本文从活性粒子动力学理论方法提供的基本描述出发,对模型进行微观-宏观推导。根据[9]中提出的定义,我们考虑所谓的奇异模型。报告的第一部分主要是对文献中已知的一些现象学模型进行调查和批判性分析。我们详细参考了一些案例研究:病毒模型的传播、社会动力学和流体中的Keller-Segel。第二部分展示了如何开发希尔伯特型方法,从活性粒子动力学理论提供的基本描述中导出宏观尺度的模型。第三部分介绍了与所选案例研究相对应的宏观模型的推导。最后,对未来的研究前景进行了展望。
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来源期刊
CiteScore
6.30
自引率
17.10%
发文量
61
审稿时长
1 months
期刊介绍: The purpose of this journal is to provide a medium of exchange for scientists engaged in applied sciences (physics, mathematical physics, natural, and technological sciences) where there exists a non-trivial interplay between mathematics, mathematical modelling of real systems and mathematical and computer methods oriented towards the qualitative and quantitative analysis of real physical systems. The principal areas of interest of this journal are the following: 1.Mathematical modelling of systems in applied sciences; 2.Mathematical methods for the qualitative and quantitative analysis of models of mathematical physics and technological sciences; 3.Numerical and computer treatment of mathematical models or real systems. Special attention will be paid to the analysis of nonlinearities and stochastic aspects. Within the above limitation, scientists in all fields which employ mathematics are encouraged to submit research and review papers to the journal. Both theoretical and applied papers will be considered for publication. High quality, novelty of the content and potential for the applications to modern problems in applied sciences and technology will be the guidelines for the selection of papers to be published in the journal. This journal publishes only articles with original and innovative contents. Book reviews, announcements and tutorial articles will be featured occasionally.
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