Mathematical Research for Models Which is Related to Chemotaxis System

Jiashan Zheng ()
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Jiashan Zheng: Ludong University, School of Mathematics and Statistics Science

Chapter Chapter 12 in Current Trends in Mathematical Analysis and Its Interdisciplinary Applications, 2019, pp 351-444 from Springer

Abstract: Abstract This paper proposes a survey and critical analysis focused on a variety of chemotaxis models in biology, namely the Chemotaxis system 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 six parts. The first part focuses on background of the models which is related to Chemotaxis system and its development. The second–five part are devoted to the qualitative analysis of the (quasilinear) Keller–Segel model, the (quasilinear) chemotaxis–haptotaxis model, the (quasilinear) chemotaxis system with consumption of chemoattractant, and the (quasilinear) Keller–Segel–Navier–Stokes system. Finally, an overview of the entire contents leads to suggestions for future research activities.

Keywords: Boundedness; Navier–Stokes system; Keller–Segel model; Chemotaxis models; Chemotaxis-haptotaxis model; Global existence; Nonlinear diffusion (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-15242-0_12

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DOI: 10.1007/978-3-030-15242-0_12

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