Global existence of solutions to a fully parabolic chemotaxis system with singular sensitivity and logistic source.

In this paper we study the global existence of solutions to the fully parabolic chemotaxis system: u t = Δ u − χ ∇ ⋅ (u v ∇ v) + f (u) , v t = Δ v − v + u in a smooth bounded domain Ω ⊂ R n (n ≥ 3) subject to the non-flux boundary conditions, where χ > 0 and the logistic function f ∈ C 1 [ 0 , ∞) satisfies f (s) ≤ r − μ s γ with r ≥ 0 and γ , μ > 0. It is shown that the problem possesses a global and classical solution as long as γ > 2. Moreover, the global existence of the weak solution is also established provided that f (s) = r s − μ s 2 with any r , μ > 0. [ABSTRACT FROM AUTHOR]