Large time behavior of solutions to a chemotaxis model with porous medium diffusion.

In this paper, we study the large time behavior of a chemotaxis model with nonlinear diffusion and consumption { u t = Δ u m − ∇ ⋅ (u ∇ v) + μ u (1 − u) , v t − Δ v = − v u , where m > 1. In a previous paper [5] , we have proved the existence and uniform boundedness of global weak solutions for any nonnegative initial data and any m > 1. In this work, we show that the weak solutions strongly converge to (1 , 0) in the large time limit. [ABSTRACT FROM AUTHOR]