Toward a mathematical theory of Keller-Segel models of pattern formation in biological tissues
Toward a mathematical theory of Keller-Segel models of pattern formation in biological tissues
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DOI：
10.1142/s021820251550044x
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发表时间：
2015-08-01
影响因子：
3.5
通讯作者：
Winkler, M.
中科院分区：
文献类型：
--
作者：
Bellomo, N.;Bellouquid, A.;Winkler, M.
本文对生物学中的各种趋化性模型，即经典的Keller-Segel模型及其后续修正进行了调查和批判性分析，在某些情况下，这些模型已被开发用于获得防止溶液非物理爆炸的模型。报告由三个部分组成。第一部分的重点是对一些样本模型的调查，即原始模型及其一些发展，如通量限制模型，或根据类似概念推导的模型。第二部分对解的存在性、爆破性和渐近性等解析问题进行定性分析。第三部分涉及从底层描述推导宏观模型，通过动态论方法提供。这种方法导致经典模型的推导和新模型的推导，就相关的分析问题而言，这可能值得注意。最后，对整个研究内容进行概述，并对未来的研究活动提出建议。
This paper proposes a survey and critical analysis focused on a variety of chemotaxis models in biology, namely the classical Keller-Segel model and its subsequent modifications, which, in several cases, have been developed to obtain models that prevent the non-physical blow up of solutions. The presentation is organized in three parts. The first part focuses on a survey of some sample models, namely the original model and some of its developments, such as flux limited models, or models derived according to similar concepts. The second part is devoted to the qualitative analysis of analytic problems, such as the existence of solutions, blow-up and asymptotic behavior. The third part deals with the derivation of macroscopic models from the underlying description, delivered by means of kinetic theory methods. This approach leads to the derivation of classical models as well as that of new models, which might deserve attention as far as the related analytic problems are concerned. Finally, an overview of the entire contents leads to suggestions for future research activities.