Identification of a chemotactic sensitivity in a coupled system

Email: renee.fister{at}murraystate.edu Corresponding author. Email: maeve.mccarthy{at}murraystate.eduReceived on July 16, 2007. Revised on March 24, 2008. Accepted on June 7, 2008. Chemotaxis is the process by which cells behave in a way thatfollows the chemical gradient. Applications to bacteria growth,tissue inflammation and vascular tumours provide a focus onoptimization strategies. Experiments can characterize the formof possible chemotactic sensitivities. This paper addressesthe recovery of the chemotactic sensitivity from these experimentswhile allowing for non-linear dependence of the parameter onthe state variables. The existence of solutions to the forwardproblem is analysed. The identification of a chemotactic parameteris determined by inverse problem techniques. Tikhonov regularizationis investigated and appropriate convergence results are obtained.Numerical results of concentration-dependent chemotactic termsare explored.