K. Renee Fister and Maeve L. McCarthy, Identification of a chemotactic sensitivity in a coupled system, Mathematical Medicine and Biology, 25 no. 3 (2008), pp. 215-232. DOI:10.1093/imammb/dqn015

Chemotaxis is the process by which cells behave in a way that follows the chemical gradient. Applications to bacteria growth, tissue inflammation and vascular tumours provide a focus on optimization strategies. Experiments can characterize the form of possible chemotactic sensitivities. This paper addresses the recovery of the chemotactic sensitivity from these experiments while allowing for non-linear dependence of the parameter on the state variables. The existence of solutions to the forward problem is analysed. The identification of a chemotactic parameter is determined by inverse problem techniques. Tikhonov regularization is investigated and appropriate convergence results are obtained. Numerical results of concentration-dependent chemotactic terms are explored.