We Consider the Chemotaxi Systems in a smooth bounded domain as follow:{ █(ut = Δu-χ∇.(u∇v)+ f (u) x ϵ Ω ,t>0 @ @τ vt =Δv-v+u x ϵ Ω ,t>0)┤ Where χ∈ and f(u) =Au - Buα generalizes the logistic function with A≥0, B>0 and α>1. First for τ=0, global existence of such solutions for any nonnegative initial data is proved under the assumption that . Moreover, boundedness properties of the constructed solutions are studied. Next we assume that 2=α, τ>0 and we consider nonnegative solutions of the Neumann
Boundary value problem for the chemotaxis system above in a smooth bounded convex domain . We will see that if B is sufficiently large then for all sufficiently smooth initial data the...