K. Renee Fister, C. Maeve McCarthy, Optimal control of a chemotaxis problem, Quarterly of Applied Mathematics, 61 (2003), pp. 193-211.
Chemotaxis is the process by which cells aggregate under the force of a chemical attractant. The cell and chemoattractant concentrations are governed by a coupled system of parabolic partial differential equations. We investigate the optimal control of the proportion of cells being generated in two settings. One involves harvesting the actual cells and the other depicts removing a proportion of the chemoattractant. The optimality system for each problem contains forward and backward reaction-diffusion and convection-diffusion equations. Numerical results are presented.