Asymptotic behavior to a chemotaxis consumption system with singular sensitivity

We consider a chemotaxis consumption system with singular sensitivity ut=u-delta(delta v), v(t)=epsilon v-uv in a bounded domain Rn with ,,epsilon>0. The global existence of classical solutions is obtained with n=1. Moreover, for any global classical solution (u,v) to the case of n,1, it is shown that v converges to 0 in the L-norm as t with the decay rate established whenever epsilon(epsilon(0),1) with epsilon 0=max{0,1- X/alpha parallel to v(0)parallel to(alpha-1)(L infinity}(Omega)).