Large-time Behavior Of Solutions To A Parabolic-elliptic Chemotaxis Model With Logistic Source

A parabolic-elliptic chemotaxis model with generalized logistic source is considered in this paper.First,based on a fixed point argument,Lp-estimate technique and Moser's iteration,it is proved that the model has a globally-in-time bounded solution iunder the assumption that the coeffieient of logistie dampening is positive.Then,under the assumptions that the coefficient of logistic dannpening is suffieienly layge and that the initial cell density has a positive lower bound,it is shown that the sohition converges to a non-zero stationary solution exponentially in L2(?)as t?? by sup-and sub?solution method and energy estimate Teehmique.