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Mathematical Research for Models Which is Related to Chemotaxis System

In: Current Trends in Mathematical Analysis and Its Interdisciplinary Applications

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  • Jiashan Zheng

    (Ludong University, School of Mathematics and Statistics Science)

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.

Suggested Citation

  • Jiashan Zheng, 2019. "Mathematical Research for Models Which is Related to Chemotaxis System," Springer Books, in: Hemen Dutta & Ljubiša D. R. Kočinac & Hari M. Srivastava (ed.), Current Trends in Mathematical Analysis and Its Interdisciplinary Applications, chapter 0, pages 351-444, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-15242-0_12
    DOI: 10.1007/978-3-030-15242-0_12
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