LAUSR

Abstract We consider a Keller-Segel type chemotaxis model with logistic growth, logarithmic sensitivity and density-dependent production/consumption rate. It is a 2 × 2 reaction-diffusion system describing the interaction of cells and a chemical signal. We study Cauchy problem for the original system and its transformed system, which is one of hyperbolic-parabolic balance laws. Our initial data are generic perturbations of a constant ground state, i.e. the initial mass of perturbation is non-zero. In the case of non-diffusive chemical, we obtain optimal L 2 time decay rates for the solution with finite initial data. In the case of diffusive chemical, optimal L 2 rates are also obtained with additional assumption on the smallness of the initial amplitude but still allowing large oscillation.