Chemotaxis and growth system with singular sensitivity function

This paper continues the study of the initial value problem of a chemotaxis-growth system. In the previous paper (Nonlinear Anal. 51 (2002) 119), we have handled the case when the sensitivity function χ(ρ) is regular. In this paper, we are concerned with the case when the function has a singularity at ρ=0 like χ(ρ)=logρ or -1ρ. We verify global existence of solutions and discuss some asymptotic behaviour of solutions.