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, ∞).