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  1. (, Recent Developments in Mathematical, Statistical and Computational Sciences)
    D. M. Kilgour et al. (Ed.)
    We consider a Keller-Segel type chemotaxis model with 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 conservation laws. In both cases of diffusive and non-diffusive chemical,we obtain optimal L^2 time decay rates for the solution. Our results improve those in Li et al. (Nonlinearity 28:2181-2210, 2015 [5]), Martinez et al. (Indiana Univ Math J 67:1383-1424, 2018 [7]). 
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