Global existence to a chemotaxis-consumption model with nonlinear diffusion and singular sensitivity

This paper deals with the chemotaxis-consumption model with singular sensitivity and nonlinear diffusion ut =. center dot (D(u). u) -.. center dot f (u) v. v , x. , t > 0, vt = v - g(u)v, x. , t > 0, under the homogenous Neumann boundary condition in a smoothbounded domain . RN(N = 2), with positive parameters., and D(u)= d(u+ e)m-1, f (u)= K(u+ e)a, g(u) = s(u+ e)ss for d, K, s, e, ss > 0, m> 1 and a. R. The main goal of this paper is to prove the existence of global classical solutions whena < N/4, ss = 1 and m > a + N/4.