Advanced search
Publication Cover
Journal of Biological Dynamics Volume 17, 2023 - Issue 1
Submit an article Journal homepage
866
Views
0
CrossRef citations to date
0
Altmetric
Research Article

A refined asymptotic result of one-dimensional flux limited Keller–Segel models

Xin XuChern Institute of Mathematics and LPMC, Nankai University, Tianjin, People's Republic of ChinaCorrespondence[email protected]
View further author information
Article: 2203165 | Received 31 Oct 2022, Accepted 11 Apr 2023, Published online: 19 Apr 2023

References

  • W. Alt, Biased random walk model for chemotaxis and related diffusion approximation, J. Math. Biol. 9 (1980), pp. 147–177.
  • E. Budrene and H. Berg, Complex patterns formed by motile cells of Escherichia coli, Nature 349 (1991), pp. 630–633.
  • X. Chen, J. Hao, X. Wang, Y. Wu, and Y. Zhang, Stability of spiky solution of Keller–Segel's minimal chemotaxis model, J. Differ. Equ. 257 (2014), pp. 3102–3134.
  • A. Chertock, A. Kurganov, X. Wang, and Y. Wu, On a chemotaxis model with saturated chemotactic flux, Kinet. Relat. Models 5 (2012), pp. 51–95.
  • T. Hillen and K. Painter, A user's guide to PDE models for chemotaxis, J. Math. Biol. 58 (2009), pp. 183–217.
  • T. Hillen, K. Painter, and C. Schmeiser, Global existence for chemotaxis with finite sampling radius, Discrete Contin. Dyn. Syst. Ser. B. 7 (2007), pp. 125–144.
  • D. Horstmann, From 1970 until present: The Keller–Segel model in chemotaxis and its consequences I, Jahresber. DMV 105 (2003), pp. 103–165.
  • D. Horstmann, From 1970 until present: The Keller–Segel model in chemotaxis and its consequences II, Jahresber. DMV 106 (2004), pp. 51–69.
  • E. Keller and L. Segel, Initiation of slime mold aggregation viewed as an instability, J. Theor. Biol.26 (1970), pp. 399–415.
  • E. Keller and L. Segel, Models for chemotaxis, J. Theor. Biol. 30 (1971), pp. 225–234.
  • H. Li, Spiky steady states of a chemotaxis system with singular sensitivity, J. Dyn. Differ. Equ. 30 (2018), pp. 1775–1795.
  • P. Liu, J.P. Shi, and Z.A. Wang, Pattern formation of the attraction-repulsion Keller–Segel system, Discrete Contin. Dyn. Syst. Ser. B 18 (2013), pp. 2597–2625.
  • H. Othmer, S.R. Dunbar, and W. Alt, Models of dispersal in biological systems, J. Math. Biol. 26 (1988), pp. 263–298.
  • K.J. Painter, P.K. Maini, and H.G. Othmer, Stripe formation in juvenile pomacanthus explained by a generalized turing mechanism with chemotaxis, Proc. Natl. Acad. Sci. 96 (1999), pp. 5549–5554.
  • C.S. Patlak, Random walk with persistence and external bias, Bull. Math. Biophys. 15 (1953), pp. 311–338.
  • B. Perthame, N. Vauchelet, and Z. Wang, The flux limited Keller–Segel system; properties and derivation from kinetic equations, Rev. Mat. Iberoam. 36 (2020), pp. 357–386.
  • G.J. Petter, H.M. Byrne, D.L.S. Mcelwain, and J. Norbury, A model of wound healing and angiogenesis in soft tissue, Math. Biosci. 136 (1996), pp. 35–63.
  • J. Saragosti, V. Calvez, N. Bournaveas, A. Buguin, P. Silberzan, and B. Perthame, Mathematical description of bacterial traveling pulses, PLoS Comput. Biol. 6 (8) (2010), Article ID e1000890.
  • Z.A. Wang, Mathematics of traveling waves in chemotaxis, Discrete Contin. Dyn. Syst. Ser. B. 18 (2013), pp. 601–641.
  • Z.A. Wang and X. Xu, Radial spiky steady states of a flux-limited Keller–Segel model: Existence, asymptotics and stability, Stud. Appl. Math. 148 (2022), pp. 1251–1273.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.