Identification of a chemotactic sensitivity in a coupled system.
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.
Fister
K Renee
KR
Department of Mathematics and Statistics, Murray State University, Murray, KY 42071, USA. renee.fister@murraystate.edu
McCarthy
Maeve L
ML
D000465:Algorithms; D018407:Bacterial Physiological Phenomena; D002633:Chemotaxis / Q000502:physiology*; D008433:Mathematics; D008954:Models, Biological; D017711:Nonlinear Dynamics