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In this paper,we consider a quasilinear parabolic-parabolic chemotaxis model with nonlinear diffusivity,aggregation and logistic damping source:■where k1 epu≤D(u) or k1 up≤D(u);k2 equ≤S(u)≤k3 equ;g(u)≤a-beku.It is proved that,if q b0 for some constant b0&