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Mathematical Research for Models Which is Related to Chemotaxis System

  • Jiashan Zheng
Chapter

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 

Notes

Acknowledgements

This work is partially supported by the Shandong Provincial Science Foundation for Outstanding Youth (No. ZR2018JL005), the National Natural Science Foundation of China (No. 11601215), the Natural Science Foundation of Shandong Province of China (No. ZR2016AQ17), and the Doctor Start-up Funding of Ludong University (No. LA2016006).

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Jiashan Zheng
    • 1
  1. 1.School of Mathematics and Statistics ScienceLudong UniversityYantaiP.R. China

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