Boundedness Of A Quasilinear Parabolic-parabolic K-S System With Logistic Source In Higher Dimension

This paper deals with a quasilinear parabolic-parabolic Keller-Segel system involving a source term with nonnegative initial data under Neumann boundary condition in a smooth bounded domain Ω (?) Rn, n≥ 3. Here,Φ is supposed to be smooth positive functions satisfying C1SP≤Φ when s≥ s0 with some s0> 1, and we assume that f is smooth on [0, ∞) fulfilling f(0)≥ 0 and f(s)<≤as — μs2 for all s> 0 with constants a≥0 and μ> 0.The model is just a critical case with the balance of logistic damping and ag-gregation effects, within this framework, it prove the boundedness of the solution. This contributes to the studies of Keller-Segel system.