We study the singular limit of a system of partial differential equations which is a model for an aggregation of amoebae subjected to three effects: diffusion, growth and chemotaxis. The limit problem involves motion by mean curvature together with a nonlocal drift term. We consider rather general initial data. We prove a generation of interface property and study the motion of interfaces. We also obtain an optimal estimate of the thickness and the location of the transition layer that develops.
"The singular limit of a chemotaxis-growth system with general initial data." Adv. Differential Equations 11 (11) 1227 - 1260, 2006.