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

Abstract

In this paper, we study the large time behavior of a chemotaxis model with nonlinear diffusion and consumption{ut=Δum−∇⋅(u∇v)+μu(1−u),vt−Δv=−vu, 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.