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Horstmann, D. and Winkler, M. (2005) Boundedness vs. Blow-Up in a Chemotaxis System. Journal of Differential Equations, 215, 52-107.
https://doi.org/10.1016/j.jde.2004.10.022

has been cited by the following article:

• TITLE: Global Bounded Solutions for the Keller-Segel Chemotaxis System with Singular Sensitivity

  AUTHORS: Khalid Ahmed Abbakar, Omer Khalil, Alhussein Mohamed, Bechir Mahamat, Abdoulaye Ali, Abeer Alhadi

  KEYWORDS: Keller-Segel System, Chemotaxis, Global Bounded Solution, Singular Sensitivity

  JOURNAL NAME: Applied Mathematics, Vol.11 No.10, October 19, 2020

  ABSTRACT: In this paper, we consider the Neumann initial-boundary value problem for the Keller-Segel chemotaxis system with singular sensitivity (0.1) is considered in a bounded domain with smooth boundary, Ω ⊂ Rn (n ≥ 1), where d1 > 0, d2 > 0 with parameter χ ∈ R. When d1 = d2 + χ, satisfying for all initial data 0 ≤ n0 ∈ C0 and 0 v0∈ W1,∞ (Ω), we prove that the problem possesses a unique global classical solution which is uniformly bounded in Ω × (0, ∞).