On the convergence rate of a reaction–diffusion equation with chemotaxis to a viscosity solution

The singular limit of an advection–reaction–diffusion equation arising from a chemotaxis–growth model equation is investigated. For a very specific initial data the convergence to the viscosity solution of a limit free boundary problem is known (Henry et al. 1999) [15]. In this work, we not only allow rather general initial data but also construct refined barriers. In some special cases, these barriers provide an O(ε|lnε|)O(ε|lnε|) estimate of the location and the thickness measured in space–time of the transition layers.