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Mathematical Medicine and Biology Advance Access originally published online on July 15, 2008
Mathematical Medicine and Biology 2008 25(3):215-232; doi:10.1093/imammb/dqn015
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© The author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Identification of a chemotactic sensitivity in a coupled system

K. Renee Fister{dagger} and Maeve L. McCarthy{ddagger}

Department of Mathematics and Statistics, Murray State University, Murray, KY 42071, USA

{dagger} Email: renee.fister{at}murraystate.edu

{ddagger} Corresponding author. Email: maeve.mccarthy{at}murraystate.edu

Received 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 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.

Keywords: inverse problem; chemotaxis; Tikhonov regularization


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