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, ∞).
Highlights
The Keller-Segel system is used to model chemotactic movement in biology [1]
( ) for all initial data 0 ≤ u0 ∈ C0 Ω and 0 < v0 ∈W 1,∞ (Ω), we prove that the problem possesses a unique global classical solution which is uniformly bounded in Ω × (0, ∞)
We presented that the Neumann initial-boundary value problem for the chemotaxis system with singular sensitivity in problem (0.1) is bounded in
Summary
The Keller-Segel system is used to model chemotactic movement in biology [1]. The mathematical study of the system has attracted great interest in recent years [2]. The Keller-Segel systems were introduced to describe the aggregation of cellular slime molds, u represents the density of the cells and v represents the concentration of a chemical substance secreted by themselves. More results on the related model with general sensitivity can be found in [9] [10] [11] [12]. In this present paper, we prove the existence of global bounded classical solutions for (1.2) without assumptions on the space dimensions or the smallness assumption on the initial data in the case d=1 d2 + χ.
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